# Quiz 14: Oscillations

Physics & Astronomy

Q 1Q 1

When an object is oscillating in simple harmonic motion in the vertical direction, its maximum speed occurs when the object
A) is at its highest point.
B) is at its lowest point.
C) is at the equilibrium point.
D) has the maximum net force exerted on it.
E) has a position equal to its amplitude.

Free

Multiple Choice

C

Q 2Q 2

A mass m hanging on a spring with a spring constant k has simple harmonic motion with a period T. If the mass is doubled to 2m, the period of oscillation
A) increases by a factor of 2.
B) decreases by a factor of 2.
C) increases by a factor of
D) decreases by a factor of
E) is not affected.

Free

Multiple Choice

C

Q 3Q 3

If F is the force, x the displacement, and k a particular constant, for simple harmonic motion we must have
A) F = -k/x

^{2 }B) F = k/x C) F = (k/x^{2})^{1/2 }D) F = -kx^{2 }E) None of these is correct.Free

Multiple Choice

E

Q 4Q 4

The frequency of a simple harmonic motion is 2.6 10

^{-4}s^{-1}. The oscillation starts (t = 0) when the displacement has its maximum positive value of 6.5 10^{-3}cm. The earliest possible time at which the particle can be found at x = -2.6 10^{-3}cm is A) 7.1 10^{-6}s B) 1.2 10^{-5}s C) 1.1 10^{-4}s D) 1.1 10^{-3}s E) 4.2 10^{-3}sFree

Multiple Choice

Q 5Q 5

A particle moving with a simple harmonic motion has its maximum displacement of +18 cm at time t = 0. The frequency of the motion is 10 s

^{-1}. At a time t = 0.65 s, the position of the particle is A) +18 cm B) zero C) -13 cm D) -18 cm E) +7.3 cmFree

Multiple Choice

Q 6Q 6

A mass m hanging on a spring with a spring constant k executes simple harmonic motion with a period T. If the same mass is hung from a spring with a spring constant of 2k, the period of oscillation
A) increases by a factor of 2.
B) decreases by a factor of 2.
C) increases by a factor of .
D) decreases by a factor of .
E) is not affected.

Free

Multiple Choice

Q 7Q 7

You want a mass that, when hung on the end of a spring, oscillates with a period of 1 s. If the spring has a spring constant of 10 N/m, the mass should be
A) 10 kg
B) kg
C) 4

^{2}(10) kg D) 10/(4^{2}) kg E) None of these is correct.Free

Multiple Choice

Q 8Q 8

The instantaneous speed of a mass undergoing simple harmonic motion on the end of a spring depends on
A) the amplitude of oscillation.
B) the frequency of oscillation.
C) the period of oscillation.
D) the time at which the speed is measured.
E) all of these

Free

Multiple Choice

Q 9Q 9

A particle moving in simple harmonic motion with a period T = 1.5 s passes through the equilibrium point at time t

_{0}= 0 with a velocity of 1.00 m/s to the right. A time t later, the particle is observed to move to the left with a velocity of 0.50 m/s. (Note the change in direction of the velocity.) The smallest possible value of the time t is A) 0.17 s B) 0.33 s C) 0.50 s D) 0.25 s E) 0.82 sFree

Multiple Choice

Q 10Q 10

A particle moving with simple harmonic motion has a maximum displacement of
+12)0 cm. The particle moves from its maximum positive to its maximum negative displacement in 2.25 s. The motion starts when the displacement is x = +12.0 cm. The time for the particle to move to x = -6.00 cm is
A) 1.70 s
B) 0.750 s
C) 1.50 s
D) 2.20 s
E) 0.983 s

Free

Multiple Choice

Q 11Q 11

The force constant of a massless spring is 25.0 N/m. A mass of 0.45 kg is oscillating in simple harmonic motion at the end of the spring with an amplitude of 0.32 m. The maximum speed of the mass is
A) 5.7 m/s
B) 56 m/s
C) 7.4 m/s
D) 2.4 m/s
E) 10 m/s

Free

Multiple Choice

Q 12Q 12

The equation for the period T of a mass m oscillating with simple harmonic motion at the end of a spring with a force constant k is . A mass m that is oscillating on a spring with a force constant of 0.52 N/m has a period of 2.1 s. On a second spring, the same mass has a period of 3.5 s. The force constant of the second spring is
A) impossible to determine because the mass is not given.
B) 0.19 N/m
C) 1.4 N/m
D) 0.31 N/m
E) 0.75 N/m

Free

Multiple Choice

Q 13Q 13

A particle with a mass of 65 g is moving with simple harmonic motion. At time t = 0, the particle is at its extreme positive displacement of 18.0 cm. The period of the motion is 0.600 s. At time t = 1.35 s, the velocity of the particle is
A) -1.9 m/s
B) zero
C) 0.84 m/s
D) +1.9 m/s
E) -0.84 m/s

Free

Multiple Choice

Q 14Q 14

A particle is oscillating with simple harmonic motion. The frequency of the motion is
10 Hz and the amplitude of the motion is 5.0 cm. As the particle passes its central equilibrium position, the acceleration of the particle is
A) 100 cm/s

^{2 }B) 1.6 10^{5}cm/s^{2 }C) 4 10^{6}cm/s^{2 }D) zero E) 3.2 10^{6}cm/s^{2 }Free

Multiple Choice

Q 15Q 15

Any body moving with simple harmonic motion is being acted on by a force that is
A) constant.
B) proportional to a sine or cosine function of the displacement.
C) proportional to the inverse square of the displacement.
D) directly proportional to the displacement.
E) proportional to the square of the displacement.

Free

Multiple Choice

Q 16Q 16

A body moves with simple harmonic motion according to the equation
X = (2/) sin(4t + /3),
Where the units are SI. At t = 2 s, the speed of the body is
A) 1/3 m/s
B) 1/ m/s
C) m/s
D) 4 m/s
E) m/s

Free

Multiple Choice

Q 17Q 17

A spring vibrates in simple harmonic motion according to the equation
X = 15 cos t
Where x is in centimeters and t is in seconds. The total number of vibrations this body makes in 10 s is
A) 0.5
B) 10
C)
D) 15
E) 5

Free

Multiple Choice

Q 18Q 18

A 2.00-kg body is attached to a spring of negligible mass and oscillates with a period of 1.00 s. The force constant of the spring is
A) 0.051 N/m
B) 0.500 N/m
C) 2.00 N/m
D) 6.28 N/m
E) None of these is correct.

Free

Multiple Choice

Q 19Q 19

A body oscillates with simple harmonic motion according to the equation
X = 6.0 cos(3t + /3)
Where the units are SI. The speed of the body when it has a displacement of
3 m is
A) m/s
B) 6 m/s
C) 9 m/s
D) m/s
E) 18 m/s

Free

Multiple Choice

Q 20Q 20

A body of mass 5.0 kg moves in simple harmonic motion according to the equation
X = 0.040 sin(30t + /6)
Where the units are SI. The period of this motion is
A) 1/30 s
B) /15 s
C) /6 s
D) 15/ s
E) 30 s

Free

Multiple Choice

Q 21Q 21

A body of mass 5.0 kg moves in simple harmonic motion according to the equation
X = 0.040 sin(30t + /6)
Where the units are SI. The maximum speed of this body is approximately
A) 0.013 m/s
B) 0.40 m/s
C) 0.60 m/s
D) 1.2 m/s
E) 30 m/s

Free

Multiple Choice

Q 22Q 22

The equation of a body in simple harmonic motion is
Y = 8.0 cos(20t + )
Where y is in centimeters and t is in seconds. The frequency of the oscillations is
A) /10 Hz
B) /4 Hz
C) 10/ Hz
D) 8 Hz
E) 20 Hz

Free

Multiple Choice

Q 23Q 23

A body of mass 0.50 kg moves in simple harmonic motion with a period of 1.5 s and an amplitude of 20 mm. Which of the following equations correctly represents this motion?
A) x = 40 cos(t/1.5) mm
B) x = 40 cos(2t/1.5) mm
C) x = 20 sin(t/1.5) mm
D) x = 20 sin(1.5t) mm
E) x = 20 sin(2t/1.5) mm

Free

Multiple Choice

Q 24Q 24

A ball moves back and forth in simple harmonic motion along a line 12 cm long. When the ball is 4 cm from the left-hand end of its path, it has an acceleration of 24 cm/s

^{2}. When the ball is 1 cm from the right-hand end of its path the magnitude of its acceleration is A) 15 cm/s^{2 }B) 30 cm/s^{2 }C) 3 cm/s^{2 }D) 60 cm/s^{2 }E) 88 cm/s^{2 }Free

Multiple Choice

Q 25Q 25

A ball moves with simple harmonic motion between points A and B. The magnitude of the acceleration of the ball at point C is 5.00 m/s

^{2}. The magnitude of the acceleration of the ball at point D is A) 1.25 m/s^{2 }B) 2.50 m/s^{2 }C) 5.00 m/s^{2 }D) 7.50 m/s^{2 }E) 10.0 m/s^{2 }Free

Multiple Choice

Q 26Q 26

A particle moves in one dimension with simple harmonic motion according to the equation
D

^{2}x/dt^{2}= - 4^{2}x Where the units are SI. Its period is A) 4^{2}s B) 2 s C) 1 s D) 1/(2) s E) 1/(4^{2}) sFree

Multiple Choice

Q 27Q 27

A body moves in simple harmonic motion with amplitude A and period T. The minimum time for the body to move from a displacement of A to A/2 is
A) T/2
B) T/4
C) T/6
D) T/12
E) T/16

Free

Multiple Choice

Q 28Q 28

The top graph represents the variation of displacement with time for a particle executing simple harmonic motion. Which curve in the bottom graph represents the variation of acceleration with time for the same particle?
A) 1
B) 2
C) 3
D) 4
E) None of these is correct.

Free

Multiple Choice

Q 29Q 29

In the following equations, a is acceleration, r is a fixed distance, s is displacement, and m is mass. Which equation describes simple harmonic motion?
A) a = -kr

^{2 }B) a = r^{2 }C) a = -ks^{-1 }D) a = 4mr^{2}/3 E) a = - 4ms/3Free

Multiple Choice

Q 30Q 30

In simple harmonic motion, the displacement x = A cos t and the acceleration a = -

^{2}x. If A = 0.25 m and the period is 0.32 s, the acceleration when t = 0.12 s is A) zero B) +3.9 m/s^{2 }C) -3.9 m/s^{2 }D) +6.8 m/s^{2 }E) -6.8 m/s^{2 }Free

Multiple Choice

Q 31Q 31

A particle moving in a circle of radius 15 cm makes 33.3 rev/min. If the particle starts on the positive x axis at time t = 0, what is the x component of the particle's velocity at time
T = 1.2 s?
A) 45 cm/s
B) -3.8 cm/s
C) 26 cm/s
D) -45 cm/s
E) 13 cm/s

Free

Multiple Choice

Q 32Q 32

Use the following to answer questions :
-The object in the diagram is in circular motion. Its position at t = 0 was (A, 0). Its frequency is f. The y component of its position is given by
A) y = y

_{0}+ v_{0y}t + at^{2 }B) y = A cos 2ft C) y = A sin ft D) y = A sin 2ft E) y = A cos ftFree

Multiple Choice

Q 33Q 33

Use the following to answer questions :
-The object in the diagram is in circular motion with frequency f. At t = 0 it was at (A, 0). The y component of its velocity is given by
A) v

_{y}2 = v_{0}_{y}2 + 2a(y - y_{0}) B) v_{y}= 2fA cos 2ft C) v_{y}= A sin ft D) v_{y}= 2fA sin 2ft E) v_{y}= A cos ftFree

Multiple Choice

Q 34Q 34

Use the following to answer questions :
-The object in the diagram is in circular motion with frequency f. At t = 0 it was at (A, 0). The y component of its acceleration is given by
A) a

_{y}= (v_{y}- v_{0}_{y})/t B) a_{y}= -(2f)^{2}A cos 2ft C) a_{y}= -(2)^{2}A sin 2t D) a_{y}= -(2f)^{2}A sin 2ft E) a_{y}= -(2)^{2}A cos 2tFree

Multiple Choice

Q 35Q 35

The acceleration of a particle moving with simple harmonic motion is given by
A = -16.0x,
Where x is in meters and a is in meters per second squared. The period of the motion is
A) 0.25 s
B) 0.392 s
C) 1.57 s
D) 4.0 s
E) 25.2 s

Free

Multiple Choice

Q 36Q 36

A body of mass M is executing simple harmonic motion with an amplitude of 8.0 cm and a maximum acceleration of 100 cm/s

^{2}. When the displacement of this body from the equilibrium position is 6.0 cm, the magnitude of the acceleration is approximately A) 8.7 cm/s^{2 }B) 21 cm/s^{2 }C) 35 cm/s^{2 }D) 17 cm/s^{2 }E) 1.3 m/s^{2 }Free

Multiple Choice

Q 37Q 37

A light spring stretches 0.13 m when a 0.35-kg mass is hung from it. The mass is pulled down from this equilibrium position an additional 0.12 m and is released. Determine the spring constant k and the amplitude of vibration.
A) 26.4 N/m and 0.37 m
B) 26.4 N/m and 0.12 m
C) 2.70 N/m and 0.25 m
D) 26.4 N/m and 0.25 m
E) 26.4 N/m and 0.13 m

Free

Multiple Choice

Q 38Q 38

A light spring stretches 0.13 m when a 0.35 kg mass is hung from it. The mass is pulled down from this equilibrium position an additional 0.15 m and then released. Determine the maximum speed of the mass.
A) 1.10 m/s
B) 2.75 m/s
C) 11.4 m/s
D) 1.25 m/s
E) 0.02 m/s

Free

Multiple Choice

Q 39Q 39

An object is moving with simple harmonic motion. When the object is displaced 4 cm from its equilibrium point, its acceleration is 20 cm/s

^{2}. Calculate the period T. A) 0.45 s B) 0.36 s C) 2.2 s D) 2.8 s E) none of the aboveFree

Multiple Choice

Q 40Q 40

An object is moving with simple harmonic motion. When the object is displaced 5 cm from its equilibrium point, its velocity is 15.0 cm/s. Calculate the amplitude of motion if its period of motion is 3.0 s.
A) 13.6 cm
B) 7.1 cm
C) 8.7 cm
D) 5.0 cm
E) none of the above

Free

Multiple Choice

Q 41Q 41

A particle is moving with SHM. If it has velocities of v

_{1}and v_{2}when it is at positions x_{1}and x_{2}from the equilibrium position respectively, then the square of the frequency of vibration (f^{2}) is given by: A) (v_{1}^{2} v_{2}^{2}) / 4 ^{2 }(x_{1}^{2} x_{2}^{2}) B) (v_{1}^{2} v_{2}^{2}) / 4 ^{2 }(x_{2}^{2} x_{1}^{2}) C) (v_{1}^{2}+ v_{2}^{2}) / 4 ^{2 }(x_{2}^{2} x_{1}^{2}) D) (v_{1}^{2}+ v_{2}^{2}) / 2 ^{2 }(x_{2}^{2}+ x_{1}^{2}) E) (v_{1}^{2}+ v_{2}^{2}) / (x_{2}^{2} x_{1}^{2})Free

Multiple Choice

Q 42Q 42

A particle is moving with SHM. If it has velocities of 6 cm/s and 2 cm/s when it is at positions 4 cm and 7 cm respectively from the equilibrium position, then calculate its period of oscillation.
A) 5.4 s
B) 6.4 s
C) 7.4 s
D) 10.8 s
E) none of the above

Free

Multiple Choice

Q 43Q 43

A simple way to test if a device can withstand high "g-force" is to attach the device to a vibrating platform. Suppose a device has to withstand up to 5g's, and the amplitude of the oscillation is 5 cm, the frequency of the vibration should be
A) 5 Hz
B) 981 Hz
C) 31.3 Hz
D) 44.3 Hz
E) 62.6 Hz

Free

Multiple Choice

Q 44Q 44

A 2.50-kg object is attached to a spring of force constant k = 4.50 kN/m. The spring is stretched 10.0 cm from equilibrium and released. What is the maximum kinetic energy of this system?
A) 45.0 J
B) 22.5 J
C) 56.0 J
D) 2.25 10

^{5}J E) 4.50 JFree

Multiple Choice

Q 45Q 45

Use the figure to answer the next problems. A spring of negligible mass and spring constant k is attached to the wall on one end, and the other end is attached to the center of mass axis of a solid sphere of mass m and radius r. The spring is stretched a distance A from equilibrium and let go. The sphere rolls freely on a smooth surface.
-The angular frequency of the oscillation is
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 46Q 46

Use the figure to answer the next problems. A spring of negligible mass and spring constant k is attached to the wall on one end, and the other end is attached to the center of mass axis of a solid sphere of mass m and radius r. The spring is stretched a distance A from equilibrium and let go. The sphere rolls freely on a smooth surface.
-What is the linear kinetic energy when the sphere is at the equilibrium position?
A)
B)
C)
D)
E) undetermined

Free

Multiple Choice

Q 47Q 47

Use the figure to answer the next problems. A spring of negligible mass and spring constant k is attached to the wall on one end, and the other end is attached to the center of mass axis of a solid sphere of mass m and radius r. The spring is stretched a distance A from equilibrium and let go. The sphere rolls freely on a smooth surface.
-What is the rotational kinetic energy when the sphere is at the equilibrium position?
A)
B)
C)
D)
E) undetermined

Free

Multiple Choice

Q 48Q 48

A mass of 0.50 kg is attached to a massless spring with a spring constant k = 600 N/m (see figure above). The system rests on a level, friction-free surface and is initially at rest. A second mass of 0.20 kg makes an elastic head-on collision with the mass attached to the spring; thereafter, the oscillating system vibrates with an amplitude of 0.25 m. What was the incident speed of the second mass?
A) 16 m/s
B) 8.7 m/s
C) 6.1 m/s
D) 11 m/s
E) 5.3 m/s

Free

Multiple Choice

Q 49Q 49

A mass attached to a spring has simple harmonic motion with an amplitude of 4.0 cm. When the mass is 2.0 cm from the equilibrium position, what fraction of its total energy is potential energy?
A) one-quarter
B) one-third
C) one-half
D) two-thirds
E) three-quarters

Free

Multiple Choice

Q 50Q 50

When the compression of a spring is doubled, the potential energy stored in the spring is
A) the same as before.
B) doubled.
C) tripled.
D) increased by a factor of 8.
E) None of these is correct.

Free

Multiple Choice

Q 51Q 51

The energy of a simple harmonic oscillator could be doubled by increasing the amplitude by a factor of
A) 0.7
B) 1.0
C) 1.4
D) 2.0
E) 4.0

Free

Multiple Choice

Q 52Q 52

A 2.5-kg object is attached to a spring of force constant k = 4.5 kN/m. The spring is stretched 10 cm from equilibrium and released. What is the kinetic energy of the mass-spring system when the mass is 5.0 cm from its equilibrium position?
A) 5.6 J
B) 11 J
C) 17 J
D) 14 J
E) 42 J

Free

Multiple Choice

Q 53Q 53

The force constant for a simple harmonic motion is k and the amplitude of the motion is A. The maximum value of the potential energy of a mass m oscillating with simple harmonic motion is
A)
B) kA

^{2 }C) kA^{2 }D) kA E) None of these is correct.Free

Multiple Choice

Q 54Q 54

When the displacement of an object in simple harmonic motion is one-quarter of the amplitude A, the potential energy is what fraction of the total energy?
A)
B)
C) 1/16
D) There is not enough information provided to answer correctly
E) None of these is correct.

Free

Multiple Choice

Q 55Q 55

If the amplitude of a simple harmonic oscillator is doubled, the total energy is
A) unchanged.
B) one-fourth as large.
C) half as large.
D) doubled.
E) quadrupled.

Free

Multiple Choice

Q 56Q 56

A mass on a spring oscillates with an amplitude of 5.0 cm. What is the position of the mass when the kinetic and potential energies are equal?
A) There is not enough information provided to answer this question.
B) 1.2 cm
C) 2.5 cm
D) 3.5 cm
E) 3.8 cm

Free

Multiple Choice

Q 57Q 57

Which of the following statements is true of a particle that is moving in simple harmonic motion?
A) The momentum of the particle is constant.
B) The kinetic energy of the particle is constant.
C) The potential energy of Earth-particle system is constant.
D) The acceleration of the particle is constant.
E) The force the particle experiences is a negative restoring force.

Free

Multiple Choice

Q 58Q 58

A body moving in simple harmonic motion has maximum acceleration when it has
A) maximum velocity.
B) maximum kinetic energy.
C) minimum potential energy.
D) minimum kinetic energy.
E) zero displacement.

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Multiple Choice

Q 59Q 59

The displacement in simple harmonic motion is a maximum when the
A) acceleration is zero.
B) velocity is a maximum.
C) velocity is zero.
D) kinetic energy is a maximum.
E) potential energy is a minimum.

Free

Multiple Choice

Q 60Q 60

In simple harmonic motion, the magnitude of the acceleration of a body is always directly proportional to its
A) displacement.
B) velocity.
C) mass.
D) potential energy.
E) kinetic energy.

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Multiple Choice

Q 61Q 61

The kinetic energy of a body executing simple harmonic motion is plotted against time expressed in terms of the period T. At t = 0, the displacement is zero. Which of the graphs most closely represents these conditions?
A) 1
B) 2
C) 3
D) 4
E) 5

Free

Multiple Choice

Q 62Q 62

The displacement of a body moving with simple harmonic motion is given by the equation
Y = A sin(2t + )
After one-quarter of a period has elapsed since t = 0, which of the following statements is correct?
A) Half the total energy of the body is kinetic energy and half is potential energy.
B) The kinetic energy is a maximum.
C) The potential energy is a maximum.
D) The total energy is a negative maximum.
E) Both kinetic and potential energies are maxima.

Free

Multiple Choice

Q 63Q 63

A system consists of a mass vibrating on the end of a spring. The total mechanical energy of this system
A) varies as a sine or cosine function.
B) is constant only when the mass is at maximum displacement.
C) is a maximum when the mass is at its equilibrium position only.
D) is constant, regardless of the displacement of the mass from the equilibrium position.
E) is always equal to the square of the amplitude.

Free

Multiple Choice

Q 64Q 64

A 2-kg mass oscillates in one dimension with simple harmonic motion on the end of a massless spring on a horizontal frictionless table according to
X = (6/) cos( t + 3)
Where the units are SI. The total mechanical energy of this system is
A) 1 J
B) 3 J
C) 5 J
D) 7 J
E) 9 J

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Multiple Choice

Q 65Q 65

A 1.0-kg mass oscillates along the x axis with simple harmonic motion. Its position as a function of time is given by
X = 2 cos(t/6 + /3)
Where the units are SI. When t = 2 s, the kinetic energy of the mass is
A)

^{2}/24 J B) ^{2}/72 J C) 2^{2}/9 J D) 4^{2}/9 J E) ^{2}/4 JFree

Multiple Choice

Q 66Q 66

A 1.81-kg block slides on a horizontal frictionless table with a speed of 1.22 m/s. It is brought to rest by compressing a spring in its path. If the spring has a force constant of 7.30 N/m, it is compressed
A) 6.89 m
B) 1.22 m
C) 1.71 m
D) 0.305 m
E) by none of these amounts

Free

Multiple Choice

Q 67Q 67

A 10-kg block starts from rest at a vertical height of 1 m on a 30º frictionless inclined plane. If the block slides down the incline and then 20 m along a frictionless horizontal surface into a fixed spring with a force constant of 100 N/m, the spring is compressed approximately
A) 1.4 m
B) 2.0 m
C) 0.33 m
D) 0.98 m
E) 2.5 m

Free

Multiple Choice

Q 68Q 68

The kinetic energy K of a body executing simple harmonic motion is plotted against time, the time being expressed in terms of the period T. The initial conditions are such that the phase angle is zero. Such a graph would most closely resemble which of the following graphs?
A) 1
B) 2
C) 3
D) 4
E) 5

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Multiple Choice

Q 69Q 69

A 0.454-kg block starts from rest and slides 3.05 m down a frictionless plane inclined at 53º to the horizontal. At the bottom it slides 9.14 m over a horizontal frictionless plane before compressing a spring (k = 14.7 N/m) a distance x and coming momentarily to rest. The value of x is approximately
A) 0.215 m
B) 1.52 m
C) 2.44 m
D) 1.83 m
E) 1.21 m

Free

Multiple Choice

Q 70Q 70

A body on a spring is vibrating in simple harmonic motion about an equilibrium position indicated by the dashed line. The figure above that shows the body with maximum acceleration is
A) 1
B) 2
C) 3
D) 4
E) 5

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Multiple Choice

Q 71Q 71

A Foucault pendulum is a simple mass-on-a-long-string pendulum suspended from a tall ceiling. It was first exhibited at the Pantheon building in Paris, and because of the rotation of Earth about its axis, the Pantheon rotates about the pendulum as the day passes. A similar pendulum set up at the North pole would show the floor below the pendulum rotating one circle in a 24hr period. If a Foucault pendulum is installed at the equator so that it originally swings in the east-west direction, after 6 hours what is the direction of the swing?
A) east-west
B) north-south
C) NE-SW
D) NW-SE
E) in any direction

Free

Multiple Choice

Q 72Q 72

A rocket ship is propelled vertically up with an acceleration of g in a uniform gravitational field. A pendulum of length 1.0 m would have a period of
A) 0
B) 2.0 s
C) 1.41 s
D) 3.1 s
E) the period is infinite

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Multiple Choice

Q 73Q 73

An 8.0-kg block is attached to a spring with a constant of 2.0 N/m. If the spring is stretched 3.0 m from its equilibrium position and released from rest, the maximum velocity attained by the mass is
A) 0.75 m/s
B) 1.5 m/s
C) 3.0 m/s
D) 4.2 m/s
E) 15 m/s

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Multiple Choice

Q 74Q 74

A 0.10-kg mass stretches a massless spring 0.20 m from its equilibrium position. If this same mass is set into vibration on this spring, the frequency is
A) 0.023 Hz
B) 1.1 Hz
C) 2.0 Hz
D) 7.0 Hz
E) 13 Hz

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Multiple Choice

Q 75Q 75

A body of mass M suspended from a spring oscillates with a period T. If the mass of the spring can be neglected, a body of mass 2M, suspended from the same spring, oscillates with a period of
A) T/2
B)
C) T
D)
E) 2T

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Multiple Choice

Q 76Q 76

A 0.5-kg mass is suspended from a massless spring that has a force constant of 79 N/m. The mass is displaced 0.1m down from its equilibrium position and released. If the downward direction is negative, the displacement of the mass as a function of time is given by
A) y = 0.1 cos(158t - )
B) y = 0.2 cos(158t - )
C) y = 0.1 cos(12.6t - )
D) y = 0.2 cos(12.6t + )
E) y = 0.1 cos(2t + )

Free

Multiple Choice

Q 77Q 77

A spring is cut in half. The ratio of the force constant of one of the halves to the force constant of the original spring is
A)
B) 1
C) 2
D) 4
E)

Free

Multiple Choice

Q 78Q 78

The mass on the end of the spring (which stretches linearly) is in equilibrium as shown. It is pulled down so that the pointer is opposite the 11-cm mark and then released. The mass experiences its maximum upward velocity at which of the following positions?
A) 3-cm mark
B) 7-cm mark
C) 1-cm mark
D) 11-cm mark
E) None of these is correct.

Free

Multiple Choice

Q 79Q 79

A mass of 2.00 kg suspended from a spring 100 cm long is pulled down 4.00 cm from its equilibrium position and released. The amplitude of vibration of the resulting simple harmonic motion is
A) 4.00 cm
B) 2.00 cm
C) 8.00 cm
D) 1.04 cm
E) 1.02 cm

Free

Multiple Choice

Q 80Q 80

Two clocks with basic timekeeping mechanisms consisting of (1) a mass on a spring and (2) a simple pendulum are taken to the top of a mountain. At the base of the mountain, they both keep perfect time. At the top of the mountain,
A) neither keeps correct time.
B) only the pendulum clock keeps correct time.
C) only the mass-spring clock keeps correct time.
D) both keep correct time.
E) Not enough information is given to answer this question.

Free

Multiple Choice

Q 81Q 81

Both a mass-spring system and a simple pendulum have a period of 1 s. Both are taken to the moon in a lunar landing module. While they are inside the module on the surface of the moon,
A) the pendulum has a period longer than 1 s.
B) the mass-spring system has a period longer than 1 s.
C) both a and b are true.
D) the periods of both are unchanged.
E) one of them has a period shorter than 1 s.

Free

Multiple Choice

Q 82Q 82

If the length of a simple pendulum with a period T is reduced to half of its original value, the new period T is approximately
A) 0.5T
B) 0.7T
C) T (unchanged)
D) 1.4T
E) 2T

Free

Multiple Choice

Q 83Q 83

To double the period of a pendulum, the length
A) must be increased by a factor of 2.
B) must be decreased by a factor of 2.
C) must be increased by a factor of .
D) must be increased by a factor of 4.
E) need not be affected.

Free

Multiple Choice

Q 84Q 84

A clock keeps accurate time when the length of its simple pendulum is L. If the length of the pendulum is increased a small amount, which of the following is true?
A) The clock will run slow.
B) The clock will run fast.
C) The clock will continue to keep accurate time.
D) The answer cannot be determined without knowing the final length of the pendulum.
E) The answer cannot be determined without knowing the percentage increase in the length of the pendulum.

Free

Multiple Choice

Q 85Q 85

A pendulum does not have simple harmonic motion if its angular amplitude

_{0}is not small. For large angular amplitudes, the period is given by T = T_{0}[1 + (1/4) sin^{2}_{0}+ (3/64) sin^{4}_{0}+ · · · ] As the angular amplitude of the pendulum gets larger, the frequency of the pendulum A) does not change. B) increases. C) decreases. D) does whatever the period does. E) changes in proportion to T_{0}.Free

Multiple Choice

Q 86Q 86

What must be the length of a simple pendulum with a period of 2.0 s if g = 9.8 m/s

^{2}? A) 99 cm B) 97 m C) 6.2 cm D) 3.1 m E) 2.0 mFree

Multiple Choice

Q 87Q 87

A pendulum has simple harmonic motion provided that
A) its bob is not too heavy.
B) the supporting string is not too long.
C) the arc through which it swings is not too small.
D) the arc through which it swings is not too large.
E) None of these is correct.

Free

Multiple Choice

Q 88Q 88

You have landed your spaceship on the moon and want to determine the acceleration due to gravity using a simple pendulum of length 1.0 m. If the period of this pendulum is
5)0 s, what is the value of g on the moon?
A) 1.3 m/s

^{2 }B) 1.6 m/s^{2 }C) 0.80 m/s^{2 }D) 0.63 m/s^{2 }E) 2.4 m/s^{2 }Free

Multiple Choice

Q 89Q 89

A simple pendulum on Earth has a period T. The period of this pendulum could be decreased by
A) increasing the mass of the pendulum bob.
B) taking the pendulum to the moon.
C) taking the pendulum to the planet Jupiter (M

_{Jupiter}= 315M_{Earth}). D) decreasing the mass of the pendulum bob. E) increasing the length of the wire supporting the pendulum.Free

Multiple Choice

Q 90Q 90

If the length of a simple pendulum is increased by 4% and the mass is decreased by 4%, the period is
A) not changed.
B) increased by 2%.
C) decreased by 4%.
D) increased by 4%.
E) decreased by 2%.

Free

Multiple Choice

Q 91Q 91

For a simple pendulum to have a period of 1 s it must have a length of
A) 1.0 m
B) 0.25 m
C) 9.8 m
D) 4.0 m
E) 2.7 m

Free

Multiple Choice

Q 92Q 92

A uniform disk (I

_{cm}= MR^{2}) of mass M and radius R is suspended from a point on its rim. If it oscillates as a physical pendulum its period is A) B) C) D) E)Free

Multiple Choice

Q 93Q 93

If the mass of a physical pendulum is doubled while its length and mass distribution remain unchanged, its period is
A) doubled.
B) multiplied by a factor of .
C) unchanged.
D) multiplied by a factor of .
E) halved.

Free

Multiple Choice

Q 94Q 94

Which of the following statements concerning the motion of a simple pendulum is incorrect?
A) The kinetic energy is a maximum when the displacement is a maximum.
B) The acceleration is a maximum when the displacement is a maximum.
C) The period is changed if the mass of the bob is doubled and the length of the pendulum is halved.
D) The time interval between conditions of maximum potential energy is one period.
E) The velocity is a maximum when the acceleration is a minimum.

Free

Multiple Choice

Q 95Q 95

The period of oscillation of a simple pendulum of length 9.8 m and mass 5.0 kg is approximately
A) 0.10 s
B) 0.16 s
C) 2.0 s
D) 5.0 s
E) 6.3 s

Free

Multiple Choice

Q 96Q 96

A long homogeneous rod can be pivoted as a physical pendulum at each of the points shown. Points at which the periods would be about the same are
A) 1 and 2
B) 3 and 4
C) 1 and 4
D) 2 and 3
E) 1, 2, 3, and 4

Free

Multiple Choice

Q 97Q 97

A pendulum is oscillating with a total mechanical energy E

_{0}. When the pendulum is at its maximum displacement, the kinetic energy K and the potential energy U are A) K = E_{0}; U = E_{0 }B) K = 0; U = E_{0 }C) K = E_{0}; U = E_{0 }D) K = E_{0}; U = 0 E) K = E_{0}; U = E_{0 }Free

Multiple Choice

Q 98Q 98

What is the length L of a simple pendulum with the same period as a physical pendulum consisting of a hoop suspended at its rim?
A) L = R
B) L = 1/R
C)
D) L = R
E) L = 2R

Free

Multiple Choice

Q 99Q 99

A simple pendulum has a mass of 10 kg. The length of the pendulum is 1.0 m. The work required to move the pendulum from its vertical position at rest to a horizontal position at rest is approximately
A) 0
B) 10 J
C) 16 J
D) 98 J
E) 1.6 kJ

Free

Multiple Choice

Q 100Q 100

The graph shows the square of the period versus the length of a simple pendulum on a certain planet. The acceleration due to gravity on that planet is approximately
A) 0.100 m/s

^{2 }B) 10.0 m/s^{2 }C) 3.95 m/s^{2 }D) 395 m/s^{2 }E) 0.628 m/s^{2 }Free

Multiple Choice

Q 101Q 101

The graph shows the period squared versus the length for a simple pendulum. The slope of the graph corresponds to
A) 1/g
B) g/(4

^{2}) C) g D) 4^{2}/g E) 4^{2}gFree

Multiple Choice

Q 102Q 102

A physical pendulum oscillates with small amplitude and a frequency of 2.00 Hz at a place where g is equal to 9.81 m/s

^{2}. The length of a simple pendulum that would oscillate with small amplitude at the same frequency is approximately A) 6.10 cm B) 12.2 cm C) 97.5 cm D) 2.44 m E) 4.88 mFree

Multiple Choice

Q 103Q 103

In the laboratory, a stick 1 m long is pivoted at various points to illustrate the motion of a physical pendulum. A plot of the period versus the distance of the pivot point from the center of mass is shown. The data presented demonstrate which of the following?
A) The motion of a pendulum is circular about the center of mass.
B) The center of mass is at 0.4 m.
C) The graph is meaningless in this form.
D) There is a minimum period in the neighborhood of 1.5 s at a pivotal distance of approximately 0.4 m from the center of mass.
E) The graph should be drawn as a straight line from A to C; point D is obviously wrong.

Free

Multiple Choice

Q 104Q 104

The graph is a plot of the period of a physical pendulum versus the distance from the pivot point to the center of mass. If the physical pendulum is suspended 44 cm from the center of mass, a simple pendulum that would have the same period would have a length of approximately
A) 19 cm
B) 30 cm
C) 44 cm
D) 49 cm
E) 63 cm

Free

Multiple Choice

Q 105Q 105

A giant simple pendulum has a time period of 5.0 s. If the time period is changed to 4.5 s, calculate the change in the length of the string if g is constant at 9.81 m/s

^{2}. A) 1.2 m shorter B) 0.8 m longer C) 1.2 m longer D) 0.8 m shorter E) None of the aboveFree

Multiple Choice

Q 106Q 106

A giant simple pendulum has a time period of 5.00 s at a particular place. If the time period is changed to 4.65 s by shortening the string by 1.0 m, calculate the acceleration due to gravity at this place.
A) 9.18 m/s

^{2 }B) 9.81 m/s^{2 }C) 9.99 m/s^{2 }D) 10.3 m/s^{2 }E) 8.31 m/s^{2 }Free

Multiple Choice

Q 107Q 107

A thin test tube is partially filled with lead pellets so that it floats vertically in a fluid. Use Archimedes' Principle to calculate that if displaced slightly from its equilibrium position the test tube will undergo SHM in the vertical direction and derive how the time period is related to the density of the fluid.
A) T proportional to (liquid)
B) T proportional to (liquid)

^{1/2 }C) T proportional to (liquid)^{2 }D) T proportional to (liquid)^{}^{2 }E) T proportional to (liquid)^{}^{1/2 }Free

Multiple Choice

Q 108Q 108

A thin test tube is partially filled with lead pellets so that it floats vertically in a fluid. When displaced slightly in the vertical direction, the tube undergoes SHM. In water the period is found to be 1.25 s, and when in an unknown fluid its period is 1.40 s. Use Archimedes' Principle to help you determine the density of the unknown liquid. (Density of water = 1 g/cm

^{3}) A) 1.1 g/cm^{3 }B) 1.2 g/cm^{3 }C) 0.89 g/cm^{3 }D) 0.80 g/cm^{3 }E) 0.94 g/cm^{3 }Free

Multiple Choice

Q 109Q 109

An oscillator has a quality factor of 300. By what percentage does its energy decrease in each cycle?
A) 0.33%
B) 1%
C) 2%
D) 3%
E) 4%

Free

Multiple Choice

Q 110Q 110

An oscillator has a quality factor of 100. By what percentage does its energy decrease in each cycle?
A) 2%
B) 3%
C) 4%
D) 5%
E) 6%

Free

Multiple Choice

Q 111Q 111

The energy of an oscillator decreases by 3% each cycle. The quality factor of this oscillator is approximately
A) 209
B) 157
C) 87
D) 63
E) 21

Free

Multiple Choice

Q 112Q 112

The energy of an oscillator decreases by 10% each cycle. The quality factor of this oscillator is approximately
A) 314
B) 157
C) 87
D) 63
E) 21

Free

Multiple Choice

Q 113Q 113

A damped oscillator has a decay time constant . After time t = has passed, the fraction of the amount of energy remaining is
A) 0.25
B) 0.37
C) 0.5
D) 0.67
E) 0.75

Free

Multiple Choice

Q 114Q 114

Use the figure to the right to answer the next problems.
A ball of mass m = 100 g and radius r = 10 cm is suspended from a light spring with spring constant k = 4 N/m. The ball is then immersed in oil with viscosity = 0.2 Pas, and set into oscillation with an initial amplitude of A = 2 cm.
-The oscillation is
A) very weakly damped.
B) weakly damped.
C) critically damped.
D) overdamped.
E) unable to tell

Free

Multiple Choice

Q 115Q 115

Use the figure to the right to answer the next problems.
A ball of mass m = 100 g and radius r = 10 cm is suspended from a light spring with spring constant k = 4 N/m. The ball is then immersed in oil with viscosity = 0.2 Pas, and set into oscillation with an initial amplitude of A = 2 cm.
-What is the angular frequency of oscillation?
A) 6.32 rad/s
B) 7.23 rad/s
C) 6.03 rad/s
D) 4.15 rad/s
E) 3.16 rad/s

Free

Multiple Choice

Q 116Q 116

Use the figure to the right to answer the next problems.
A ball of mass m = 100 g and radius r = 10 cm is suspended from a light spring with spring constant k = 4 N/m. The ball is then immersed in oil with viscosity = 0.2 Pas, and set into oscillation with an initial amplitude of A = 2 cm.
-What is the amplitude after 1 s?
A) 2 cm
B) 0.63 cm
C) 0.96 cm
D) 0.30 cm
E) 0.15 cm

Free

Multiple Choice

Q 117Q 117

When driving over a washboard speed bumps, certain speeds make the bumps less "bumpy." Suppose your car has mass of 1000 kg and the critical damping constant of the shock absorbers is 12000 kg/s, what is the "ideal speed" to drive across the bumps assuming that the bumps are 0.3 m apart? Hint: Find the decay time for the critically damped shock absorbers.
A) 1.2 m/s
B) 2.4 m/s
C) 3.6 m/s
D) 4.8 m/s
E) 6 m/s

Free

Multiple Choice

Q 118Q 118

Which of the following statements is true for a simple harmonic oscillator that is not subject to dissipative forces?
A) The potential energy of the system attains a maximum value when the displacement is one-half the amplitude.
B) The kinetic energy of the system attains a maximum value when the acceleration has the greatest absolute value.
C) The total mechanical energy of the system decreases as the mass slows down and increases as the mass speeds up.
D) The total mechanical energy of the system is equal to the maximum value of the kinetic energy of the system.
E) The period of the oscillation varies inversely as the displacement amplitude.

Free

Multiple Choice

Q 119Q 119

Use the following to answer questions :
-The graph shows the average power delivered to an oscillating system as a function of the driving frequency. According to these data
A) the resonant frequency is greater than

_{o}. B) the system corresponding to curve 1 has the largest quality factor. C) the system corresponding to curve 4 has the largest quality factor. D) the resonant frequency is less than _{o}. E) None of these is correct.Free

Multiple Choice

Q 120Q 120

Use the following to answer questions :
-The graph shows the average power delivered to an oscillating system as a function of the driving frequency. According to these data
A) the resonant frequency is greater than

_{o}. B) the system corresponding to curve 1 has the smallest quality factor. C) the system corresponding to curve 4 has the smallest quality factor. D) the resonant frequency is less than _{o}. E) None of these is correct.Free

Multiple Choice

Q 121Q 121

Use the following to answer questions :
-The graph shows the average power delivered to an oscillating system as a function of the driving frequency. According to these data, the damping is greatest for system(s)
A) 1
B) 2
C) 3
D) 4
E) 1 and 2

Free

Multiple Choice

Q 122Q 122

Use the following to answer questions :
-The graph shows the average power delivered to an oscillating system as a function of the driving frequency. According to these data, the damping is least for system(s)
A) 1
B) 2
C) 3
D) 4
E) 3 and 4

Free

Multiple Choice

Q 123Q 123

The differential equation for a damped oscillator is If the damping is not too large, the time constant for the motion of this oscillator is determined by the
A) spring constant k and the mass m of the system.
B) spring constant k and the damping coefficient b of the system.
C) mass m and the damping coefficient b of the system.
D) initial displacement of the system.
E) initial velocity of the system.

Free

Multiple Choice

Q 124Q 124

The solution to the differential equation of a damped oscillator, for the case in which the damping is small, is
X = A

_{0}e^{-(}^{b}^{/2}^{m}^{)}^{t}cos('t + ) The phase constant is determined by the A) spring constant k and the mass m of the system. B) spring constant k and the damping coefficient b of the system. C) initial velocity of the system. D) initial displacement of the system. E) c and dFree

Multiple Choice

Q 125Q 125

Use the following to answer questions :
-The graph shows the displacement of an oscillator as a function of time. The oscillator that is critically damped is
A) 1
B) 2
C) 3
D) 4
E) 1, 2, 3, and 4

Free

Multiple Choice

Q 126Q 126

Use the following to answer questions :
-The graph shows the displacement of an oscillator as a function of time. The oscillator that is undamped is
A) 1
B) 2
C) 3
D) 4
E) 1, 2, 3, and 4

Free

Multiple Choice

Q 127Q 127

Use the following to answer questions :
-The graph shows the displacement of an oscillator as a function of time. The oscillator that is overdamped is
A) 1
B) 2
C) 3
D) 4
E) 1, 2, 3, and 4

Free

Multiple Choice

Q 128Q 128

When you push a child in a swing, you most likely
A) push with as large a force as possible.
B) push with a periodic force as often as possible.
C) push with a periodic force, with a period that depends on the weight of the child.
D) push with a periodic force, with a period that depends on the length of the ropes on the swing.
E) push with a force equal to the weight of the child.

Free

Multiple Choice

Q 129Q 129

The shattering of a crystal glass by an intense sound is an example of
A) resonance.
B) a Q factor.
C) critical damping.
D) an exponential decrease.
E) overdamping.

Free

Multiple Choice

Q 130Q 130

When a body capable of oscillating is acted on by a periodic series of impulses having a frequency equal to one of the natural frequencies of oscillation of the body, the body is set in vibration with relatively large amplitude. This phenomenon is known as
A) beats.
B) harmonics.
C) overtones.
D) resonance.
E) pressure amplitude.

Free

Multiple Choice

Q 131Q 131

The graph shows the response of a driven oscillatory system as a function of time. The region(s) of the graph that show(s) the steady-state response is(are)
A) 1
B) 2
C) 3
D) 1 and 2
E) 2 and 3

Free

Multiple Choice

Q 132Q 132

The graph shows the response of a driven oscillatory system as a function of time. The region(s) of the graph that show(s) only the transient response is (are)
A) 1
B) 2
C) 3
D) 1 and 2
E) 2 and 3

Free

Multiple Choice

Q 133Q 133

Near resonance, if the damping is small (large Q), the oscillator
A) absorbs less energy from the driving force than it does at other frequencies.
B) absorbs more energy from the driving force than it does at other frequencies.
C) absorbs the same amount of energy from the driving force than it does at other frequencies.
D) moves with a small amplitude.
E) is described by none of these

Free

Multiple Choice

Q 134Q 134

The width of a resonance curve is an indication of
A) the damping of the system.
B) the Q-value of the system.
C) the extent to which the system is oscillatory.
D) the rate at which energy is being dissipated each cycle.
E) all of the above

Free

Multiple Choice

Q 135Q 135

The order, from highest to lowest, of the frequencies of the oscillatory systems shown in the figure is
A) a, b, c
B) b, a, c
C) c, b, a
D) c, a, b
E) a, c, b

Free

Multiple Choice

Q 136Q 136

The order, from shortest to longest, of the periods of the oscillatory systems shown in the figure above is
A) a, b, c
B) b, a, c
C) c, b, a
D) c, a, b
E) a, c, b

Free

Multiple Choice

Q 137Q 137

Use the figure to the right to answer the next problems.
A ball of mass m = 100 g and radius r = 10 cm is suspended from a light spring with spring constant k = 4 N/m. The ball is then immersed in oil with viscosity = 0.2 Pas and driven at the resonant frequency by a variable force F = F

_{o}cos (t) at an amplitude of A = 10 cm. -What is the value of F_{o}? A) 0.12 N B) 0.24 N C) 0.056 N D) 1.8 N E) 0.67 NFree

Multiple Choice

Q 138Q 138

Use the figure to the right to answer the next problems.
A ball of mass m = 100 g and radius r = 10 cm is suspended from a light spring with spring constant k = 4 N/m. The ball is then immersed in oil with viscosity = 0.2 Pas and driven at the resonant frequency by a variable force F = F

_{o}cos (t) at an amplitude of A = 10 cm. -How much energy is dissipated per cycle? A) 0.028 J B) 0.057 J C) 0.11 J D) 0.068 J E) 0.16 JFree

Multiple Choice