Question 1

A child is swinging on a playground swing, modeled as a simple pendulum. At the highest point of the swing, which of the following statements is true about the energies involved?

Accepted Answer

The potential energy is at a maximum and the kinetic energy is zero.

Question 2

A 0.025 kg mass stretches a spring by 0.05 m. What is the spring constant $$k of $$the spring? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$k = 4.9\ \mathrm{N/m}$$

Question 3

Which of the following changes will increase the frequency of a mass-spring oscillator?

Accepted Answer

Increasing the spring constant.

Question 4

A pendulum clock is designed so that one complete period is $$2.00\ \mathrm{s}. $$What should the length $$L of $$the pendulum be? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$L = 0.99\ \mathrm{m}$$

Question 5

Which of the following best describes the energy transformation in a simple harmonic oscillator with no damping?

Accepted Answer

Potential energy is constantly converted to kinetic energy, with the total energy remaining constant.

Question 6

A mass on a spring oscillates with a frequency $$f = \frac{1}{2\pi}\sqrt{\frac{k}{m}}. If $$the mass is quadrupled, what happens to the frequency?

Accepted Answer

It decreases by a factor of 2.

Question 7

A physical pendulum has its center of gravity at a distance $$d$$ from the pivot and moment of inertia $$I. $$Which change will increase its frequency?

Accepted Answer

Increasing the distance $$d$$ while keeping $$I$$ constant.

Question 8

A pendulum is released from rest at its maximum displacement. At what point during its swing is the acceleration of the mass the greatest?

Accepted Answer

At the highest points of the swing.

Question 9

A mass oscillates on a spring. At which point is the kinetic energy a maximum?

Accepted Answer

At the equilibrium position.

Question 10

A ball on a massless, rigid rod oscillates as a simple pendulum with a period of $$2.0\ \mathrm{s}. If $$the ball is replaced with another ball having twice the mass, what is the new period?

Accepted Answer

$$2.0\ \mathrm{s}$$

Question 11

A damped oscillator has its amplitude decrease according to $$x_{max}(t) = Ae$$^{-t/	au}$$. What is the amplitude after a time t = 2$$	au$$?

Accepted Answer

$$A/e^2$$

Question 12

A train car experiences large amplitude rocking due to resonance with the frequency of bumps on the track. Which action will eliminate the resonance?

Accepted Answer

Change the speed of the train so the driving frequency no longer matches the natural frequency.

Question 13

Which of the following statements about resonance is correct?

Accepted Answer

Resonance occurs when the driving frequency matches the natural frequency, resulting in large amplitude oscillations.

Question 14

A mass-spring system is oscillating with little damping. What happens to the amplitude if the damping is increased significantly?

Accepted Answer

The amplitude decreases more rapidly.

Question 15

A student models their leg as a uniform rod of length $$L$$ pivoted at one end. What is the period $$T of $$the leg's swinging motion as a physical pendulum?

Accepted Answer

$$T = 2\pi\sqrt{\frac{2L}{3g}}$$

Question 16

Which of the following will NOT affect the period of a simple pendulum?

Accepted Answer

The mass of the pendulum bob.

Question 17

A mass on a spring is oscillating vertically. At which point is the acceleration zero?

Accepted Answer

At the equilibrium position.

Question 18

A pendulum is swinging with a small amplitude. Which change will decrease its frequency?

Accepted Answer

Increasing the length of the pendulum.

Question 19

A mass-spring system is driven at a frequency much higher than its natural frequency. What is the amplitude of oscillation compared to resonance?

Accepted Answer

It is much smaller than at resonance.

Question 20

Which of the following best describes the effect of damping on a resonance curve?

Accepted Answer

Damping broadens the resonance curve and decreases the maximum amplitude.

Oscillations, Simple Harmonic Motion, and Resonance

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