# Quiz 15: Oscillations

Physics & Astronomy

Q 1Q 1

A particle oscillating in simple harmonic motion is:
A)never in equilibrium because it is in motion
B)never in equilibrium because there is a force
C)in equilibrium at the ends of its path because its velocity is zero there
D)in equilibrium at the center of its path because the acceleration is zero there
E)in equilibrium at the ends of its path because the acceleration is zero there

Free

Multiple Choice

D

Q 2Q 2

An object is undergoing simple harmonic motion.Throughout a complete cycle it:
A)has constant speed
B)has varying amplitude
C)has varying period
D)has varying acceleration
E)has varying mass

Free

Multiple Choice

D

Q 3Q 3

When a body executes simple harmonic motion, its acceleration at the ends of its path must be:
A)zero
B)less than g
C)more than g
D)suddenly changing in sign
E)none of these

Free

Multiple Choice

E

Q 4Q 4

A weight suspended from an ideal spring oscillates up and down with a period T.If the amplitude of the oscillation is doubled, the period will be:
A)T
B)1.5 T
C)2T
D)T/2
E)4T

Free

Multiple Choice

Q 5Q 5

It is impossible for two particles, each executing simple harmonic motion, to remain in phase with each other if they have different:
A)masses
B)periods
C)amplitudes
D)spring constants
E)kinetic energies

Free

Multiple Choice

Q 6Q 6

An oscillatory motion must be simple harmonic if:
A)the amplitude is small
B)the potential energy is equal to the kinetic energy
C)the motion is along the arc of a circle
D)the acceleration varies sinusoidally with time
E)the derivative, dU/dx, of the potential energy is negative

Free

Multiple Choice

Q 7Q 7

A particle is in simple harmonic motion with period T.At time t = 0 it is at the equilibrium point.At the times listed below it is at various points in its cycle.Which of them is farthest away from the equilibrium point?
A)0.5T
B)0.7T
C)T
D)1.4T
E)1.5T

Free

Multiple Choice

Q 8Q 8

A particle moves back and forth along the x axis from x = -x

_{m}to x = +x_{m}, in simple harmonic motion with period T.At time t = 0 it is at x = +x_{m}.When t = 0.75T: A)it is at x = 0 and is traveling toward x = +x_{m}B)it is at x = 0 and is traveling toward x = -x_{m}C)it is at x = +x_{m}and is at rest D)it is between x = 0 and x = +x_{m}and is traveling toward x = -x_{m}E)it is between x = 0 and x = -x_{m}and is traveling toward x = -x_{m}Free

Multiple Choice

Q 9Q 9

A particle is in simple harmonic motion with period T.At time t=0 it is halfway between the equilibrium point and an end point of its motion, travelling toward the end point.The next time it is at the same place is:
A)t = T
B)t = T/2
C)t = T/3
D)t = T/4
E)none of the above

Free

Multiple Choice

Q 10Q 10

An object attached to one end of a spring makes 20 complete vibrations in 10s.Its period is:
A)2 Hz
B)10 s
C)0.5 Hz
D)2 s
E)0.50 s

Free

Multiple Choice

Q 11Q 11

An object attached to one end of a spring makes 20 vibrations in 10 seconds.Its frequency is:
A)2 Hz
B)10 s
C)0.05 Hz
D)2 s
E)0.50 s

Free

Multiple Choice

Q 12Q 12

An object attached to one end of a spring makes 20 vibrations in 10 seconds.Its angular frequency is:
A)0.79 rad/s
B)1.57 rad/s
C)2.0 rad/s
D)6.3 rad/s
E)12.6 rad/s

Free

Multiple Choice

Q 13Q 13

Frequency f and angular frequency are related by
A)f =
B)f = 2
C)f = /
D)f = /2
E)f = 2/

Free

Multiple Choice

Q 14Q 14

A block attached to a spring oscillates in simple harmonic motion along the x axis.The limits of its motion are x = 10 cm and x = 50 cm and it goes from one of these extremes to the other in 0.25 s.Its amplitude and frequency are:
A)40 cm, 2 Hz
B)20 cm, 4 Hz
C)40 cm, 4 Hz
D)25 cm, 4 Hz
E)20 cm, 2 Hz

Free

Multiple Choice

Q 15Q 15

This plot shows a mass oscillating as x = x

_{m}cos (ωt + φ).What are x_{m}and φ? A)1 m, 0° B)2 m, 0° C)2 m, 90° D)4 m, 0° E)4 m, 90°Free

Multiple Choice

Q 16Q 16

The amplitude and phase constant of an oscillator are determined by:
A)the frequency
B)the angular frequency
C)the initial displacement alone
D)the initial velocity alone
E)both the initial displacement and velocity

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Multiple Choice

Q 17Q 17

In simple harmonic motion, the displacement is maximum when the:
A)acceleration is zero
B)velocity is maximum
C)velocity is zero
D)kinetic energy is maximum
E)momentum is maximum

Free

Multiple Choice

Q 18Q 18

Two identical undamped oscillators have the same amplitude of oscillation only if:
A)they are started with the same displacement x

_{0}B)they are started with the same velocity v_{0}C)they are started with the same phase D)they are started so the combination is the same E)they are started so the combination is the sameFree

Multiple Choice

Q 19Q 19

The amplitude of any oscillator will be doubled by:
A)doubling only the initial displacement
B)doubling only the initial speed
C)doubling the initial displacement and halving the initial speed
D)doubling the initial speed and halving the initial displacement
E)doubling both the initial displacement and the initial speed

Free

Multiple Choice

Q 20Q 20

A particle moves in simple harmonic motion according to x = 2cos(50t), where x is in meters and t is in seconds.Its maximum velocity is:
A)100 sin(50t)m/s
B)100 cos(50t)m/s
C)100 m/s
D)200 m/s
E)none of these

Free

Multiple Choice

Q 21Q 21

A 0.20-kg object mass attached to a spring whose spring constant is 500 N/m executes simple harmonic motion.If its maximum speed is 5.0 m/s, the amplitude of its oscillation is:
A)0.0020 m
B)0.10 m
C)0.20 m
D)25 m
E)250 m

Free

Multiple Choice

Q 22Q 22

The acceleration of a body executing simple harmonic motion leads the velocity by what phase?
A)0 rad
B)/8 rad
C)/4 rad
D)/2 rad
E) rad

Free

Multiple Choice

Q 23Q 23

In simple harmonic motion, the magnitude of the acceleration is greatest when:
A)the displacement is zero
B)the displacement is maximum
C)the speed is maximum
D)the force is zero
E)the speed is between zero and its maximum

Free

Multiple Choice

Q 24Q 24

In simple harmonic motion:
A)the acceleration is greatest at the maximum displacement
B)the velocity is greatest at the maximum displacement
C)the period depends on the amplitude
D)the acceleration is constant
E)the acceleration is greatest at zero displacement

Free

Multiple Choice

Q 25Q 25

In simple harmonic motion, the magnitude of the acceleration is:
A)constant
B)proportional to the displacement
C)inversely proportional to the displacement
D)greatest when the velocity is greatest
E)never greater than g

Free

Multiple Choice

Q 26Q 26

A 1.2-kg mass is oscillating without friction on a spring whose spring constant is 3400 N/m.When the mass's displacement is 7.2 cm, what is its acceleration?
A)−3.8 m/s

^{2}B)−200 m/s^{2}C)−240 m/s^{2}D)−2.0 x 10^{4}m/s^{2}E)cannot be calculated without more informationFree

Multiple Choice

Q 27Q 27

The displacement of an object oscillating on a spring is given by x(t)= x

_{m}cos(t + ).If the initial displacement is zero and the initial velocity is in the negative x direction, then the phase constant is: A)0 radians B)/2 radians C) radians D)3/2 radians E)2 radiansFree

Multiple Choice

Q 28Q 28

The displacement of an object oscillating on a spring is given by x(t)= x

_{m}cos(t + ).If the object is initially displaced in the negative x direction and given a negative initial velocity, then the phase constant is between: A)0 and /2 radians B)/2 and radians C) and 3/2 radians D)3/2 and 2 radians E)none of the above ( is exactly 0, /2, , or 3/2 radians)Free

Multiple Choice

Q 29Q 29

A certain spring elongates 9 mm when it is suspended vertically and a block of mass M is hung on it.The angular frequency of this mass-spring system:
A)is 0.088 rad/s
B)is 33 rad/s
C)is 200 rad/s
D)is 1140 rad/s
E)cannot be computed unless the value of M is given

Free

Multiple Choice

Q 30Q 30

A 3-kg block, attached to a spring, executes simple harmonic motion according to x = 2cos(50t)where x is in meters and t is in seconds.The spring constant of the spring is:
A)1 N/m
B)100 N/m
C)150 N/m
D)7500 N/m
E)none of these

Free

Multiple Choice

Q 31Q 31

In simple harmonic motion, the restoring force must be proportional to the:
A)amplitude
B)frequency
C)velocity
D)displacement
E)displacement squared

Free

Multiple Choice

Q 32Q 32

Let U be the potential energy (with the zero at zero displacement)and K be the kinetic energy of a simple harmonic oscillator.U

_{avg}and K_{avg}are the average values over a cycle.Then: A)K_{avg}> U_{avg}B)K_{avg}< U_{avg}C)K_{avg}= U_{avg}D)K = 0 when U = 0 E)K + U = 0Free

Multiple Choice

Q 33Q 33

A particle is in simple harmonic motion along the x axis.The amplitude of the motion is x

_{m}.At one point in its motion its kinetic energy is K = 5 J and its potential energy (measured with U = 0 at x = 0)is U = 3 J.When it is at x = x_{m}, the kinetic and potential energies are: A)K = 5 J and U = 3 J B)K = 5 J and U = -3 J C)K = 8 J and U = 0 J D)K = 0 J and U = 8 J E)K = 0 J and U = -8 JFree

Multiple Choice

Q 34Q 34

A particle is in simple harmonic motion along the x axis.The amplitude of the motion is x

_{m}.When it is at x = x_{1}, its kinetic energy is K = 5 J and its potential energy (measured with U = 0 at x = 0)is U = 3 J.When it is at x = -1/2 x_{m}, the kinetic and potential energies are: A)K = 6 J and U = 2 J B)K = 6 J and U = -2 J C)K = 8 J and U = 0 J D)K = 0 J and U = 8 J E)K = 0 J and U = -8 JFree

Multiple Choice

Q 35Q 35

A 0.25-kg block oscillates on the end of the spring with a spring constant of 200 N/m.If the system has an energy of 6.0 J, then the amplitude of the oscillation is:
A)0.06 m
B)0.17 m
C)0.24 m
D)4.9 m
E)6.9 m

Free

Multiple Choice

Q 36Q 36

A 0.25-kg block oscillates on the end of the spring with a spring constant of 200 N/m.If the system has an energy of 6.0 J, then the maximum speed of the block is:
A)0.06 m/s
B)0.17 m/s
C)0.24 m/s
D)4.9 m/s
E)6.9 m/s

Free

Multiple Choice

Q 37Q 37

A 0.25-kg block oscillates on the end of the spring with a spring constant of 200 N/m.If the oscillation is started by elongating the spring 0.15 m and giving the block a speed of 3.0 m/s, then the maximum speed of the block is:
A)0.13 m/s
B)0.18 m/s
C)3.7 m/s
D)5.2 m/s
E)13 m/s

Free

Multiple Choice

Q 38Q 38

A 0.25-kg block oscillates on the end of the spring with a spring constant of 200 N/m.If the oscillation is started by elongating the spring 0.15 m and giving the block a speed of 3.0 m/s, then the amplitude of the oscillation is:
A)0.13 m
B)0.18 m
C)3.7 m
D)5.2 m
E)13 m

Free

Multiple Choice

Q 39Q 39

An object on the end of a spring is set into oscillation by giving it an initial velocity while it is at its equilibrium position.In the first trial the initial velocity is v

_{0}and in the second it is 4v_{0}.In the second trial: A)the amplitude is half as great and the maximum acceleration is twice as great B)the amplitude is twice as great and the maximum acceleration is half as great C)both the amplitude and the maximum acceleration are twice as great D)both the amplitude and the maximum acceleration are four times as great E)the amplitude is four times as great and the maximum acceleration is twice as greatFree

Multiple Choice

Q 40Q 40

A block attached to a spring undergoes simple harmonic motion on a horizontal frictionless surface.Its total energy is 50 J.When the displacement is half the amplitude, the kinetic energy is:
A)0 J
B)12.5 J
C)25 J
D)37.5 J
E)50 J

Free

Multiple Choice

Q 41Q 41

A particle is in simple harmonic motion along the x axis.The amplitude of the motion is x

_{m}.When it is at x = x_{1}, its kinetic energy is K = 5 J and its potential energy (measured with U = 0 at x = 0)is U = 3 J.When it is at x = -1/2 x_{m}, its total energy is: A)0 J B)3 J C)4 J D)5 J E)8 JFree

Multiple Choice

Q 42Q 42

A particle is in simple harmonic motion along the x axis.The amplitude of the motion is x

_{m}.When it is at x = x_{1}, its kinetic energy is K = 5 J and its potential energy (measured with U = 0 at x = 0)is U = 3 J.When its kinetic energy is 8 J, it is at: A)x = 0 B)x = x_{1}C)x = x_{m}/2 D)x = x_{m}/ E)x = x_{m}Free

Multiple Choice

Q 43Q 43

A particle is in simple harmonic motion along the x axis.The amplitude of the motion is x

_{m}.When it is at x = x_{1}, its kinetic energy is K = 5 J and its potential energy (measured with U = 0 at x = 0)is U = 3 J.When its potential energy is 8 J, it is at: A)x = 0 B)x = x_{1}C)x = x_{m}/2 D)x = x_{m}/ E)x = x_{m}Free

Multiple Choice

Q 44Q 44

An angular simple harmonic oscillator:
A)oscillates at an angle to the x axis
B)oscillates along the y axis
C)involves an angular displacement and a restoring torque
D)involves an angular displacement and a restoring force
E)involves a linear displacement and a restoring torque

Free

Multiple Choice

Q 45Q 45

An angular simple harmonic oscillator is displaced 5.2 x 10

^{-2}rad from its equilibrium position.If the torsion constant is 1200 N∙m/rad, what is the torque? A)12 N∙m B)23 N∙m C)43 N∙m D)52 N∙m E)62 N∙mFree

Multiple Choice

Q 46Q 46

A disk whose rotational inertia is 450 kg∙m

^{2}hangs from a wire whose torsion constant is 2300 N∙m/rad.What is the angular frequency of its torsional oscillations? A)0.20 rad/s B)0.44 rad/s C)1.0 rad/s D)2.3 rad/s E)5.1 rad/sFree

Multiple Choice

Q 47Q 47

A disk whose rotational inertia is 450 kg∙m

^{2}hangs from a wire whose torsion constant is 2300 N∙m/rad.When its angular displacement is −0.23 rad, what is its angular acceleration? A)1.0 x 10^{-2}rad/s^{2}B)4.5 x 10^{-2}rad/s^{2}C)0.23 rad/s^{2}D)0.52 rad/s^{2}E)1.2 rad/s^{2}Free

Multiple Choice

Q 48Q 48

The amplitude of oscillation of a simple pendulum is increased from 1 to 4.Its maximum acceleration changes by a factor of:
A)1/4
B)1/2
C)2
D)4
E)16

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Multiple Choice

Q 49Q 49

A simple pendulum consists of a small ball tied to a string and set in oscillation.As the pendulum swings the tension in the string is:
A)constant
B)a sinusoidal function of time
C)the square of a sinusoidal function of time
D)the reciprocal of a sinusoidal function of time
E)none of the above

Free

Multiple Choice

Q 50Q 50

Three physical pendulums, with masses m

_{1}, m_{2}= 2m_{1}, and m_{3}= 3m_{1}, have the same shape and size and are suspended at the same point.Rank them according to their periods, from shortest to longest. A)1, 2, 3 B)3, 2, 1 C)2, 3, 1 D)2, 1, 3 E)All three are the sameFree

Multiple Choice

Q 51Q 51

Five hoops are each pivoted at a point on the rim and allowed to swing as physical pendulums.The masses and radii are Order the hoops according to the periods of their motions, smallest to largest.
A)1, 2, 3, 4, 5
B)5, 4, 3, 2, 1
C)1, 2, 3, 5, 4
D)1, 2, 5, 4, 3
E)5, 4, 1, 2, 3

Free

Multiple Choice

Q 52Q 52

Which of the following is NOT required for a simple pendulum undergoing simple harmonic oscillation?
A)a point mass
B)a massless string
C)a small amplitude
D)gravitational force
E)a large spring constant

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Multiple Choice

Q 53Q 53

If the length of a simple pendulum is doubled, its period will:
A)halve
B)increase by a factor of
C)decrease by a factor of
D)double
E)remain the same

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Multiple Choice

Q 54Q 54

A simple pendulum of length L and mass M has frequency f.To increase its frequency to 2f:
A)increase its length to 4L
B)increase its length to 2L
C)decrease its length to L/2
D)decrease its length to L/4
E)decrease its mass to < M/4

Free

Multiple Choice

Q 55Q 55

A simple pendulum has length L and period T.As it passes through its equilibrium position, the string is suddenly clamped at its mid-point.The period then becomes:
A)2T
B)T
C)T/2
D)T/4
E)none of the above

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Multiple Choice

Q 56Q 56

Which of the following is the difference between a simple pendulum and a physical pendulum?
A)The physical pendulum does not rotate around its center of mass.
B)The physical pendulum does not depend on the acceleration of gravity.
C)The physical pendulum has an extended mass.
D)The simple pendulum has a small amplitude.
E)The physical pendulum rotates around its center of mass.

Free

Multiple Choice

Q 57Q 57

A meter stick is pivoted at a point a distance a from its center and swings as a physical pendulum.Of the following values for a, which results in the shortest period of oscillation?
A)a = 0.1 m
B)a = 0.2 m
C)a = 0.3 m
D)a = 0.4 m
E)a = 0.5 m

Free

Multiple Choice

Q 58Q 58

Two uniform spheres are pivoted on horizontal axes that are tangent to their surfaces.The one with the longer period of oscillation is the one with:
A)the larger mass
B)the smaller mass
C)the larger rotational inertia
D)the smaller rotational inertia
E)the larger radius

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Multiple Choice

Q 59Q 59

At the instant its angular displacement is 0.32 rad, the angular acceleration of a physical pendulum is -630 rad/s

^{2}.What is its angular frequency of oscillation? A)6.6 rad/s B)14 rad/s C)20 rad/s D)44 rad/s E)200 rad/sFree

Multiple Choice

Q 60Q 60

The angular displacement of a simple pendulum is given by θ(t)= θ

_{m}cos (ωt + φ).If the pendulum is 45 cm in length, and is given an angular speed dθ/dt = 3.4 rad/s at time t = 0, when it is hanging vertically, what is θ_{m}? A)4.6 rad B)3.4 rad C)1.4 rad D)0.73 rad E)0.45 radFree

Multiple Choice

Q 61Q 61

The period of a simple pendulum is 1 s on Earth.When brought to a planet where g is one-tenth that on Earth, its period becomes:
A)1 s
B)s
C)1/10 s
D)s
E)10 s

Free

Multiple Choice

Q 62Q 62

The rotational inertia of a uniform thin rod about its end is ML

^{2}/3, where M is the mass and L is the length.Such a rod is hung vertically from one end and set into small amplitude oscillation.If L = 1.0 m this rod will have the same period as a simple pendulum of length: A)33 cm B)50 cm C)67 cm D)100 cm E)150 cmFree

Multiple Choice

Q 63Q 63

Both the x and y coordinates of a point execute simple harmonic motion.The result might be a circular orbit if:
A)the amplitudes are the same but the frequencies are different
B)the amplitudes and frequencies are both the same
C)the amplitudes and frequencies are both different
D)the phase constants are the same but the amplitudes are different
E)the amplitudes and the phase constants are both different

Free

Multiple Choice

Q 64Q 64

Both the x and y coordinates of a point execute simple harmonic motion.The frequencies are the same but the amplitudes are different.The resulting orbit might be:
A)an ellipse
B)a circle
C)a parabola
D)a hyperbola
E)a square

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Multiple Choice

Q 65Q 65

For an oscillator subjected to a damping force proportional to its velocity:
A)the displacement is a sinusoidal function of time
B)the velocity is a sinusoidal function of time
C)the frequency is a decreasing function of time
D)the mechanical energy is constant
E)none of the above is true

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Multiple Choice

Q 66Q 66

A particle undergoes damped harmonic motion.The spring constant is 100 N/m; the damping constant is 8.0 x 10

^{-3}kg∙m/s, and the mass is 0.050 kg.If the particle starts at its maximum displacement, x = 1.5 m, at time t = 0, what is the particle's position at t = 5.0 s? A)-1.5 m B)-0.73 m C)0 m D)0.73 m E)1.5 mFree

Multiple Choice

Q 67Q 67

A particle undergoes damped harmonic motion.The spring constant is 100 N/m; the damping constant is 8.0 x 10

^{-3}kg∙m/s, and the mass is 0.050 kg.If the particle starts at its maximum displacement, x = 1.5 m, at time t = 0, what is the amplitude of the motion at t = 5.0 s? A)1.5 m B)1.3 m C)1.0 m D)0.67 m E)0.24 mFree

Multiple Choice

Q 68Q 68

A particle undergoes damped harmonic motion.The spring constant is 100 N/m; the damping constant is 8.0 x 10

^{-3}kg∙m/s, and the mass is 0.050 kg.If the particle starts at its maximum displacement, x = 1.5 m, at time t = 0, what is the angular frequency of the oscillations? A)4.0 rad/s B)8.0 rad/s C)12 rad/s D)23 rad/s E)45 rad/sFree

Multiple Choice

Q 69Q 69

Five particles undergo damped harmonic motion.Values for the spring constant k, the damping constant b, and the mass m are given below.Which leads to the smallest rate of loss of mechanical energy?
A)k = 100 N/m, m = 50 g, b = 8 g∙m/s
B)k = 150 N/m, m = 50 g, b = 5 g∙m/s
C)k = 150 N/m, m = 10 g, b = 8 g∙m/s
D)k = 200 N/m, m = 8 g, b = 6 g∙m/s
E)k = 100 N/m, m = 2 g, b = 4 g∙m/s

Free

Multiple Choice

Q 70Q 70

Below are sets of values for the spring constant k, damping constant b, and mass m for a particle in damped harmonic motion.Which of the sets takes the longest time for its mechanical energy to decrease to one-fourth of its initial value?

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Multiple Choice

Q 71Q 71

An oscillator is subjected to a damping force that is proportional to its velocity.A sinusoidal force is applied to it.After a long time:
A)its amplitude is an increasing function of time
B)its amplitude is a decreasing function of time
C)its amplitude is constant
D)its amplitude is a decreasing function of time only if the damping constant is large
E)its amplitude increases over some portions of a cycle and decreases over other portions

Free

Multiple Choice

Q 72Q 72

A block on a spring is subjected to an applied sinusoidal force AND to a damping force that is proportional to its velocity.The energy dissipated by damping is supplied by:
A)the potential energy of the spring
B)the kinetic energy of the mass
C)gravity
D)friction
E)the applied force

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Multiple Choice

Q 73Q 73

An oscillator is driven by a sinusoidal force.The frequency of the applied force:
A)must be equal to the natural frequency of the oscillator
B)becomes the natural frequency of the oscillator
C)must be less than the natural frequency of the oscillator
D)must be greater than the natural frequency of the oscillator
E)is independent of the natural frequency of the oscillator

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Multiple Choice

Q 74Q 74

A sinusoidal force with a given amplitude is applied to an oscillator.At resonance the amplitude of the oscillation is limited by:
A)the damping force
B)the initial amplitude
C)the initial velocity
D)the force of gravity
E)none of the above

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Multiple Choice

Q 75Q 75

A sinusoidal force with a given amplitude is applied to an oscillator.To maintain the largest amplitude oscillation the frequency of the applied force should be:
A)half the natural frequency of the oscillator
B)the same as the natural frequency of the oscillator
C)twice the natural frequency of the oscillator
D)unrelated to the natural frequency of the oscillator
E)determined from the maximum speed desired

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Multiple Choice