Question 1

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 2

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/?

Accepted Answer

The maximum acceleration is directly proportional to the square of the frequency. So, if the frequency doubles, the maximum acceleration will increase by a factor of 4.

Question 3

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 4

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 5

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 pendulum is dependent on the square root of the length and the mass. With a decreased mass and increased length, the period of the pendulum will be less than T. Therefore, option D is the correct answer.

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 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 7

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 8

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

The frequency is the number of drips per second. So, the frequency is 40 drips / 30.0 s = 1.33 Hz. The closest answer choice is 1.3 Hz.

Question 9

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 10

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 11

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 12

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 13

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

If the clock is running fast, the pendulum is swinging too quickly, so to slow it down, the weight needs to be lowered, which increases the effective length of the pendulum, decreasing its frequency.

Question 14

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 acceleration on the pendulum will be the vector sum of the acceleration due to gravity and the upward acceleration of the elevator. As the acceleration due to gravity remains constant, the effective length of the pendulum will increase, which will decrease the period of the pendulum. Therefore, the period of the pendulum decreases.

Question 15

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 multiply the frequency by 60 (since there are 60 seconds in a minute).

Number of oscillations per minute = 512 Hz x 60 = 30,720

Therefore the closest answer choice is A) 30,700.

Question 16

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 17

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 18

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 pendulum depends only on its length and the acceleration due to gravity, not on the velocity or acceleration of the elevator. Therefore, the period of the pendulum remains constant even if the elevator is moving upward with constant velocity.

Question 19

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 20

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...

Quiz 14: Oscillations

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

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?

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 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?

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

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

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?

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

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

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?