Question 1

A guitar string is set into vibration with a frequency of 512 Hz. How many oscillations does it undergo each minute?
A) 30,700
B) 8.53
C) 26.8
D) 1610
E) 512

Accepted Answer

To find the number of oscillations per minute, we need to convert the frequency from Hz (oscillations per second) to oscillations per minute. There are 60 seconds in a minute, so:
512 oscillations per second x 60 seconds per minute = 30,720 oscillations per minute
Rounding to the nearest hundred, the answer is 30,700, which is choice A.

Question 2

A sewing machine needle moves up and down in simple harmonic motion with an amplitude of 1.27 cm and a frequency of 2.55 Hz. What are the (a) maximum speed and (b) maximum acceleration of the tip of the needle?

Accepted Answer

The answer of A sewing machine needle moves up and...

Question 3

The position of a cart that is oscillating on a spring is given by the equation x = (12.3 cm) cos[(1.26 s^-1)t]. When t = 0.805 s, what are the (a) velocity and (b) acceleration of the cart?

Accepted Answer

The answer of The position of a cart that is...

Question 4

A point on the string of a violin moves up and down in simple harmonic motion with an amplitude of 1.24 mm and a frequency of 875 Hz.
(a) What is the maximum speed of that point in SI units?
(b) What is the maximum acceleration of the point in SI units?

Accepted Answer

The answer of A point on the string of a...

Question 5

A leaky faucet drips 40 times in $30.0 \mathrm {~s}$ What is the frequency of the dripping?
A) 1.3 Hz
B) 0.75 Hz
C) 1.6 Hz
D) 0.63 Hz

Accepted Answer

Frequency is the number of occurrences of a repeating event per unit time. In this case, the event is the dripping of the faucet, and the unit time is one second. The frequency of the dripping is therefore:$$f = \frac{40 \mathrm{~drips}}{30.0 \mathrm{~s}} = 1.33 \mathrm{~Hz}$$Therefore, the correct answer is A.

Question 6

A simple pendulum and a mass oscillating on an ideal spring both have period T in an elevator at rest. If the elevator now moves downward at a uniform 2 m/s, what is true about the periods of these two systems?
A) Both periods would remain the same.
B) Both periods would increase.
C) Both periods would decrease.
D) The period of the pendulum would increase but the period of the spring would stay the same.
E) The period of the pendulum would decrease but the period of the spring would stay the same.

Accepted Answer

The period of a simple pendulum depends on the length of the pendulum and the acceleration due to gravity, neither of which changes in an elevator moving downward at a constant speed. The period of a mass oscillating on an ideal spring depends on the mass and the spring constant, which also do not change in this scenario. Therefore, both periods remain the same.

Question 7

A simple pendulum that consists of a small ball of mass m and a massless wire of length L swings with a period T. Suppose now that the mass is rearranged so that mass of the ball was reduced but the mass of the wire was increased, with the total mass remaining m and the length being L. What is true about the new period of swing? (There could be more than one correct choice.)
A) The new period is T because the total mass m has not changed.
B) The new period is T because the length L has not changed.
C) The new period is greater than T.
D) The new period is less than T
E) The new period is T because neither L nor m have changed.

Accepted Answer

The period of a simple pendulum is given by T=2π(L/g)^1/2, where L is the length of the pendulum and g is the acceleration due to gravity. Since the total mass m remains constant and the length L also remains constant, the only factor that affects the period of the pendulum is g. When the mass of the ball is reduced, the new center of mass will be closer to the pivot point, which will reduce the effective length of the pendulum, making it swing faster and decreasing the period of the pendulum. Therefore, the new period will be less than T.

Question 8

If a pendulum makes 12 complete swings in 8.0 s, what are its (a) frequency and (b) period?

Accepted Answer

The answer of If a pendulum makes 12 complete swings...

Question 9

Grandfather clocks are designed so they can be adjusted by moving the weight at the bottom of the pendulum up or down. Suppose you have a grandfather clock at home that runs fast. Which of the following adjustments of the weight would make it more accurate? (There could be more than one correct choice.)
A) Raise the weight.
B) Lower the weight.
C) Add more mass to the weight.
D) Remove some mass from the weight.
E) Decrease the amplitude of swing by a small amount.

Accepted Answer

The time it takes for the pendulum to swing back and forth is determined by the length of the pendulum. By lowering the weight, the effective length of the pendulum is increased, making the clock run more slowly and therefore more accurate. Raising the weight would do the opposite and make the clock run even faster. Adding or removing mass from the weight would have no effect on the clock's accuracy. Decreasing the amplitude of the swing would also have little effect on accuracy, as long as the swing is still wide enough for the escapement mechanism to function properly.

Question 10

A pendulum of length L is suspended from the ceiling of an elevator. When the elevator is at rest the period of the pendulum is T. How does the period of the pendulum change when the elevator moves upward with constant velocity?
A) The period does not change.
B) The period increases.
C) The period decreases.
D) The period becomes zero.
E) The period increases if the upward acceleration is more than g/2 but decreases if the upward acceleration is less than g/2.

Accepted Answer

The period of a simple pendulum does not depend on the mass of the pendulum or on the amplitude of the oscillation, but only on the length of the pendulum and the acceleration due to gravity (represented by g). Therefore, as the elevator moves upward with constant velocity, the length of the pendulum and the acceleration due to gravity remain constant, so the period of the pendulum also remains constant.

Question 11

A simple pendulum and a mass oscillating on an ideal spring both have period T in an elevator at rest. If the elevator now accelerates downward uniformly at 2 m/s², what is true about the periods of these two systems? A) Both periods would remain the same. B) Both periods would increase. C) Both periods would decrease. D) The period of the pendulum would increase but the period of the spring would stay the same. E) The period of the pendulum would decrease but the period of the spring would stay the same.

Accepted Answer

The period of a simple pendulum depends on the acceleration due to gravity (g). If the elevator accelerates downward, the effective acceleration due to gravity decreases, leading to an increase in the pendulum's period. The period of a mass on a spring depends on the mass and the spring constant, not on gravity, so it remains unchanged.

Question 12

A pendulum of length L is suspended from the ceiling of an elevator. When the elevator is at rest the period of the pendulum is T. How would the period of the pendulum change if the supporting chain were to break, putting the elevator into freefall?
A) The period does not change.
B) The period increases slightly.
C) The period decreases slightly.
D) The period becomes zero.
E) The period becomes infinite because the pendulum would not swing.

Accepted Answer

When the elevator is in freefall, both the pendulum and the elevator are in a state of freefall, experiencing the same acceleration due to gravity. This means there is no force to restore the pendulum to its equilibrium position, so it would not swing at all. Hence, the concept of a period for the pendulum's motion does not apply, effectively making it infinite because the pendulum does not initiate any oscillatory motion.

Question 13

If your heart is beating at 76.0 beats per minute, what is the frequency of your heart's oscillations in hertz?
A) 4560 Hz
B) 1450 Hz
C) 3.98 Hz
D) 2.54 Hz
E) 1.27 Hz

Accepted Answer

The frequency in hertz (Hz) is the number of cycles (or beats) per second. To convert beats per minute to hertz, divide the number of beats by 60 seconds. Therefore, 76.0 beats per minute is 76.0/60 = 1.27 Hz.

Question 14

If the frequency of a system undergoing simple harmonic motion doubles, by what factor does the maximum value of acceleration change?
A) 4
B) 2
C) $\sqrt { 2 }$
D) 2/π

Accepted Answer

The maximum acceleration in simple harmonic motion is proportional to the square of the frequency. If the frequency doubles, the maximum acceleration increases by a factor of $2^2 = 4$.

Question 15

If a floating log is seen to bob up and down 15 times in 1.0 min as waves pass by you, what are the frequency and period of the wave?

Accepted Answer

The answer of If a floating log is seen to...

Question 16

A sewing machine needle moves in simple harmonic motion with a frequency of 2.5 Hz and an amplitude of 1.27 cm.
(a) How long does it take the tip of the needle to move from the highest point to the lowest point in its travel?
(b) How long does it take the needle tip to travel a total distance of 11.43 cm?

Accepted Answer

The answer of A sewing machine needle moves in simple...

Question 17

A pendulum of length L is suspended from the ceiling of an elevator. When the elevator is at rest the period of the pendulum is T. How does the period of the pendulum change when the elevator moves downward with constant acceleration?
A) The period does not change.
B) The period increases.
C) The period decreases.
D) The period becomes zero.
E) The period increases if the upward acceleration is more than g/2 but decreases if the upward acceleration is less than g/2.

Accepted Answer

The answer of A pendulum of length L is suspended...

Question 18

The quartz crystal in a digital watch has a frequency of 32.8 kHz. What is its period of oscillation?
A) 30.5 µs
B) 15.3 µs
C) 95.8 µs
D) 0.191 ms
E) 9.71 µs

Accepted Answer

The period of oscillation can be calculated using the formula: T = 1/frequency
T = 1/32.8 kHz = 30.5 µs (as 1 kHz = 1000 Hz)

Question 19

An object is undergoing simple harmonic motion of amplitude 2.3 m. If the maximum velocity of the object is 10 m/s, what is the object's angular frequency?
A) 4.3 rad/s
B) 4.8 rad/s
C) 3.5 rad/s
D) 4.0 rad/s

Accepted Answer

The maximum velocity $v_{max}$ in simple harmonic motion is given by $v_{max} = \omega A$, where $\omega$ is the angular frequency and $A$ is the amplitude. Rearranging for $\omega$, we get $\omega = \frac{v_{max}}{A} = \frac{10 \, \text{m/s}}{2.3 \, \text{m}} \approx 4.3 \, \text{rad/s}$.

Question 20

A pendulum of length L is suspended from the ceiling of an elevator. When the elevator is at rest the period of the pendulum is T. How does the period of the pendulum change when the elevator moves upward with constant acceleration?
A) The period does not change.
B) The period increases.
C) The period decreases.
D) The period becomes zero.
E) The period increases if the upward acceleration is more than g/2 but decreases if the upward acceleration is less than g/2.

Accepted Answer

When the elevator moves upward with constant acceleration, the effective gravitational force on the pendulum decreases. This is because the acceleration of the elevator is adding to the gravitational force, resulting in a net force smaller than g. As a result, the period of the pendulum decreases. This effect is more pronounced the larger the acceleration of the elevator, so choice E is not correct.

Quiz 14: Oscillations

A guitar string is set into vibration with a frequency of 512 Hz. How many oscillations does it undergo each minute?

A sewing machine needle moves up and down in simple harmonic motion with an amplitude of 1.27 cm and a frequency of 2.55 Hz. What are the (a) maximum speed and (b) maximum acceleration of the tip of the needle?

The position of a cart that is oscillating on a spring is given by the equation x = (12.3 cm) cos[(1.26 s-1)t]. When t = 0.805 s, what are the (a) velocity and (b) acceleration of the cart?

A point on the string of a violin moves up and down in simple harmonic motion with an amplitude of 1.24 mm and a frequency of 875 Hz. (a) What is the maximum speed of that point in SI units? (b) What is the maximum acceleration of the point in SI units?

A leaky faucet drips 40 times in 30.0 s30.0 \mathrm {~s}30.0 s What is the frequency of the dripping?

A simple pendulum and a mass oscillating on an ideal spring both have period T in an elevator at rest. If the elevator now moves downward at a uniform 2 m/s, what is true about the periods of these two systems?

If a pendulum makes 12 complete swings in 8.0 s, what are its (a) frequency and (b) period?

A pendulum of length L is suspended from the ceiling of an elevator. When the elevator is at rest the period of the pendulum is T. How does the period of the pendulum change when the elevator moves upward with constant velocity?

A simple pendulum and a mass oscillating on an ideal spring both have period T in an elevator at rest. If the elevator now accelerates downward uniformly at 2 m/s2, what is true about the periods of these two systems?

A pendulum of length L is suspended from the ceiling of an elevator. When the elevator is at rest the period of the pendulum is T. How would the period of the pendulum change if the supporting chain were to break, putting the elevator into freefall?

If your heart is beating at 76.0 beats per minute, what is the frequency of your heart's oscillations in hertz?

If the frequency of a system undergoing simple harmonic motion doubles, by what factor does the maximum value of acceleration change?

If a floating log is seen to bob up and down 15 times in 1.0 min as waves pass by you, what are the frequency and period of the wave?

A pendulum of length L is suspended from the ceiling of an elevator. When the elevator is at rest the period of the pendulum is T. How does the period of the pendulum change when the elevator moves downward with constant acceleration?

The quartz crystal in a digital watch has a frequency of 32.8 kHz. What is its period of oscillation?

An object is undergoing simple harmonic motion of amplitude 2.3 m. If the maximum velocity of the object is 10 m/s, what is the object's angular frequency?

A pendulum of length L is suspended from the ceiling of an elevator. When the elevator is at rest the period of the pendulum is T. How does the period of the pendulum change when the elevator moves upward with constant acceleration?

The position of a cart that is oscillating on a spring is given by the equation x = (12.3 cm) cos[(1.26 s^-1)t]. When t = 0.805 s, what are the (a) velocity and (b) acceleration of the cart?

A leaky faucet drips 40 times in $30.0 \mathrm {~s}$ What is the frequency of the dripping?

A simple pendulum and a mass oscillating on an ideal spring both have period T in an elevator at rest. If the elevator now accelerates downward uniformly at 2 m/s², what is true about the periods of these two systems?