Q: A 0.5 kg block slides on a frictionless surface and compresses a spring with $$k = 245\ \mathrm{N/m}. If $$its speed is $$1.32\ \mathrm{m/s}$$ before contact, what is the maximum compression $$x of $$the spring?

$$x = \sqrt{\frac{m v^2$}{k}} = \sqrt{\frac{0.5 \times (1.32)^2$}{245}} \approx 0.053\ \mathrm{m}$$

Question 1

A mass on a spring completes 10 oscillations in 18 seconds. What is the frequency of the oscillation?

Accepted Answer

$$f = \frac{10}{18} = 0.56\ \mathrm{Hz}$$

Question 2

Which of the following best describes simple harmonic motion (SHM)?

Accepted Answer

Motion where the restoring force is proportional and opposite to displacement

Question 3

A block of mass $$m is $$attached to a spring with spring constant $$k. $$What is the period of oscillation for this system?

Accepted Answer

$$T = 2\pi \sqrt{\frac{m}{k}}$$

Question 4

If the amplitude of a simple harmonic oscillator is doubled, what happens to the period?

Accepted Answer

The period remains unchanged

Question 5

A mass-spring system oscillates with $$x(t) = A \cos(\omega t). $$What is the maximum velocity of the mass?

Accepted Answer

$$v_{	ext{max}} = A\omega$$

Question 6

Which of the following statements about the energy in a simple harmonic oscillator is correct?

Accepted Answer

The total mechanical energy is constant and equal to $$\frac{1}{2}kA^2$

Question 7

A simple pendulum of length $$L is $$oscillating with small amplitude. What is its period?

Accepted Answer

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

Question 8

A grandfather clock runs slow. To make it run faster, should you raise or lower the pendulum weight?

Accepted Answer

Raise the weight to shorten the pendulum

Question 9

For a mass-spring system, what is the relationship between the angular frequency $$\omega$$ and the spring constant $$k$$ and mass $$m$$?

Accepted Answer

$$\omega = \sqrt{\frac{k}{m}}$$

Question 10

A damped oscillator has an amplitude that decreases over time. Which equation describes the amplitude of an underdamped oscillator?

Accepted Answer

$$A = A_0$ e$$^{-bt/2m}$$

Question 11

Which of the following best describes resonance in a driven oscillator?

Accepted Answer

The amplitude is maximized when the driving frequency equals the natural frequency

Question 12

A 0.5 kg block slides on a frictionless surface and compresses a spring with $$k = 245\ \mathrm{N/m}. If $$its speed is $$1.32\ \mathrm{m/s}$$ before contact, what is the maximum compression $$x of $$the spring?

Accepted Answer

$$x = \sqrt{\frac{m v^2$}{k}} = \sqrt{\frac{0.5 	imes (1.32)^2$}{245}} \approx 0.053\ \mathrm{m}$$

Question 13

For a simple harmonic oscillator, at which position is the velocity maximum?

Accepted Answer

At the equilibrium position ($$x = 0)$$

Question 14

A pendulum of length $$L is $$taken to a planet where $$g is $$four times that on Earth. How does the period change?

Accepted Answer

The period becomes half as long

Question 15

Which of the following is true for the total mechanical energy $$E of a $$simple harmonic oscillator (no damping)?

Accepted Answer

$$E = \frac{1}{2}kA^2$

Question 16

A mass-spring system is critically damped. What is the behavior of the system?

Accepted Answer

It returns to equilibrium without oscillating

Question 17

If a system is overdamped, what happens to its return to equilibrium compared to a critically damped system?

Accepted Answer

It returns to equilibrium more slowly

Question 18

A child is pushed on a swing at regular intervals, maintaining a constant amplitude. This is an example of:

Accepted Answer

A damped driven oscillator

Question 19

What is the angular speed $$\omega$$ for a mass-spring system with period $$T$$?

Accepted Answer

$$\omega = \frac{2\pi}{T}$$

Question 20

Which of the following is a correct statement about the frequency of a simple pendulum?

Accepted Answer

It is independent of the mass of the pendulum

Oscillations About Equilibrium (Chapter 13) – PHYS 1021 Study Notes

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