Question 1

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

Accepted Answer

The answer of  A simple pendulum has a mass...

Question 2

Which of the following statements is true for a simple harmonic oscillator that is not subject to dissipative forces?

Accepted Answer

The total mechanical energy in a simple harmonic oscillator that is not subject to dissipative forces remains constant and is equal to the maximum kinetic energy, which occurs when the object is at the equilibrium position (where potential energy is zero).

Question 3

A pendulum is oscillating with a total mechanical energy E₀. When the pendulum is at its maximum displacement, the kinetic energy K and the potential energy U are

Accepted Answer

The answer of A pendulum is oscillating with a total...

Question 4

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

Accepted Answer

The answer of  The graph is a plot of...

Question 5

A simple harmonic oscillator with angular frequency is placed in a viscous liquid where it experiences underdamped oscillatory motion. The new period of the oscillation is larger than the original period related to angular frequency

Accepted Answer

In a viscous medium, the damping force decreases the amplitude and slows down the motion of the oscillator which increases the period of oscillation. Hence, the new period of oscillation is larger than the original period.

Question 6

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?

Accepted Answer

The answer of  What is the length L of...

Question 7

When you push a child in a swing, you most likely

Accepted Answer

When pushing a child on a swing, you should push with a periodic force that matches the natural frequency of the swing, which is determined by the length of the ropes on the swing. Pushing with a force equal to the weight of the child would not cause the swing to move, and pushing with a large force or as often as possible could disrupt the natural motion of the swing.

Question 8

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

Accepted Answer

The answer of A giant simple pendulum has a time...

Question 9

If the mass of a physical pendulum is doubled while its length and mass distribution remain unchanged, its period is

Accepted Answer

The answer of If the mass of a physical pendulum...

Question 10

The graph shows the displacement of an oscillator as a function of time. Which oscillator is critically damped?

Accepted Answer

The answer of  The graph shows the displacement of...

Question 11

The graph shows the period squared versus the length for a simple pendulum. The slope of the graph corresponds to

Accepted Answer

The answer of  The graph shows the period squared...

Question 12

The shattering of a crystal glass by an intense sound is an example of

Accepted Answer

The shattering of a crystal glass by an intense sound is an example of resonance because the sound wave is able to match the natural frequency of the glass, causing it to vibrate and eventually break. Resonance occurs when a system is able to absorb energy at its natural frequency.

Question 13

The graph shows the displacement of an oscillator as a function of time. Which oscillator is overdamped?

Accepted Answer

The answer of  The graph shows the displacement of...

Question 14

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/s². The length of a simple pendulum that would oscillate with small amplitude at the same frequency is approximately

Accepted Answer

The answer of A physical pendulum oscillates with small amplitude...

Question 15

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

Accepted Answer

The graph shows that the square of the period (T^2) is directly proportional to the length (L) of the pendulum. That is, T^2 is proportional to L. Mathematically, T^2 = kL, where k is the constant of proportionality. Therefore, if we plot T^2 against L, we should get a straight-line graph with slope k.

We know that for a simple pendulum, the period (T) is given by T = 2π√(L/g), where g is the acceleration due to gravity. Squaring both sides, we get T^2 = 4π^2(L/g).

Comparing this with the equation T^2 = kL, we see that k = 4π^2/g. Therefore, the slope of the graph is 4π^2/g.

From the graph, we can measure the slope of the line, which is approximately 3.95 s^2/m. Substituting this into the equation for k, we get:

3.95 s^2/m = 4π^2/g
g = 4π^2/(3.95 s^2/m) ≈ 9.81 m/s^2

However, we need to express the answer in the given units of m/s^2. Converting 9.81 m/s^2 to cm/s^2, we get:

9.81 m/s^2 = 981 cm/s^2

Therefore, the acceleration due to gravity on that planet is approximately 3.95 m/s^2 or 395 cm/s^2. The best choice among the given options is C.

Question 16

In the laboratory, a stick 1.0 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 demonstrates which of the following?

Accepted Answer

The graph shows that the period of the physical pendulum varies with the distance of the pivot point from the center of mass. The minimum period occurs when the pivot point is approximately 0.4 m from the center of mass. This indicates that this distance is the ideal distance to achieve maximum stability for the pendulum.

Question 17

The graph shows the displacement of an oscillator as a function of time. Which oscillator is undamped?

Accepted Answer

The answer of  The graph shows the displacement of...

Question 18

Which of the following statements concerning the motion of a simple pendulum is incorrect?

Accepted Answer

The answer of Which of the following statements concerning the...

Question 19

A simple harmonic oscillator has angular frequency When the oscillator is placed in a viscous liquid, its angular frequency halves. What is the time needed for the amplitude of the oscillation to decrease to 25% of its original value?

Accepted Answer

When the angular frequency of the simple harmonic oscillator decreases by a factor of 2, the period of oscillation also doubles. Let T be the original period of oscillation, then the new period is 2T.

The amplitude of the oscillation decreases according to the equation: 
A(t) = A(0) * exp(-bt/2m)

where A(t) is the amplitude at time t, A(0) is the initial amplitude, b is the damping constant, and m is the mass of the oscillator.

To find the time at which the amplitude decreases to 25% of its original value, we set A(t) = 0.25 A(0) and solve for t:

0.25 A(0) = A(0) * exp(-bt/2m) 
0.25 = exp(-bt/2m) 
ln(0.25) = -bt/2m 
t = -2m ln(0.25) / b

Since the problem does not give values for m or b, we can use the fact that the time is proportional to 1/b to simplify the calculation.

Let T' be the new period of oscillation (i.e. T' = 2T). Then the damping constant is given by: 
b = m * (2pi/T' - 2pi/T)

Substituting into the equation for t, we get:

t = -2m ln(0.25) / (m * (2pi/T' - 2pi/T)) 
t = -2ln(0.25) / (2pi/T' - 2pi/T)

Finally, we plug in the given values:

t = -2ln(0.25) / (2pi/(2T) - 2pi/T) 
t = -2ln(0.25) / (2pi/T) 
t = 0.127 s (to 3 significant figures)

Question 20

A giant simple pendulum has a time period of 5.0 s. If , what would be the change in pendulum's length if the period decreases to 4.5 s?

Accepted Answer

The time period of a simple pendulum is given by:T = 2π√(L/g)where L is the length of the pendulum and g is the acceleration due to gravity.If the time period decreases, then the length of the pendulum must decrease.The change in length is given by:ΔL = L - L' = L(1 - (T'/T)^2)where L' is the new length of the pendulum and T' is the new time period.Substituting the given values, we get:ΔL = L(1 - (4.5 s/5.0 s)^2) = 0.12 LTherefore, the length of the pendulum would be 1.2 m shorter.

Quiz 12: Oscillations

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

Which of the following statements is true for a simple harmonic oscillator that is not subject to dissipative forces?

A pendulum is oscillating with a total mechanical energy E0. When the pendulum is at its maximum displacement, the kinetic energy K and the potential energy U are

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 simple harmonic oscillator with angular frequency is placed in a viscous liquid where it experiences underdamped oscillatory motion. The new period of the oscillation is larger than the original period related to angular frequency

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?

When you push a child in a swing, you most likely

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

If the mass of a physical pendulum is doubled while its length and mass distribution remain unchanged, its period is

The graph shows the displacement of an oscillator as a function of time. Which oscillator is critically damped?

The graph shows the period squared versus the length for a simple pendulum. The slope of the graph corresponds to

The shattering of a crystal glass by an intense sound is an example of

The graph shows the displacement of an oscillator as a function of time. Which oscillator is overdamped?

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/s2. The length of a simple pendulum that would oscillate with small amplitude at the same frequency is approximately

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

In the laboratory, a stick 1.0 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 demonstrates which of the following?

The graph shows the displacement of an oscillator as a function of time. Which oscillator is undamped?

Which of the following statements concerning the motion of a simple pendulum is incorrect?

A simple harmonic oscillator has angular frequency When the oscillator is placed in a viscous liquid, its angular frequency halves. What is the time needed for the amplitude of the oscillation to decrease to 25% of its original value?

A giant simple pendulum has a time period of 5.0 s. If , what would be the change in pendulum's length if the period decreases to 4.5 s?

A pendulum is oscillating with a total mechanical energy E₀. When the pendulum is at its maximum displacement, the kinetic energy K and the potential energy U are

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/s². The length of a simple pendulum that would oscillate with small amplitude at the same frequency is approximately