Question 1

A mass attached to a spring oscillates with amplitude $$A$$ and period $$T. $$What is the total distance traveled by the mass after one complete period?

Accepted Answer

$$4A$$

Question 2

The restoring force for a mass-spring system is given by $$F = -kx. $$What does the negative sign indicate?

Accepted Answer

The force acts opposite to the displacement, restoring equilibrium.

Question 3

A simple pendulum has length $$L$$ and is oscillating with small amplitude. What is the correct formula for its period?

Accepted Answer

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

Question 4

If the spring constant $$k of a $$mass-spring system is doubled but the total mechanical energy is kept constant, what happens to the amplitude $$A$$?

Accepted Answer

It decreases by a factor of $$\sqrt{2}$$

Question 5

A pendulum is moved from Earth to the Moon. How does its period change?

Accepted Answer

The period increases

Question 6

A mass oscillates on a vertical spring with period $$T. If $$the entire system is taken to the Moon, what happens to the period?

Accepted Answer

The period remains the same

Question 7

Which of the following best describes resonance in a forced oscillation system?

Accepted Answer

The amplitude increases significantly when the driving frequency matches the natural frequency.

Question 8

For a simple harmonic oscillator, the displacement as a function of time is given by $$x(t) = A \cos(\omega t + \phi). $$What is the velocity as a function of time?

Accepted Answer

$$v(t) = -\omega A \sin(\omega t + \phi)$$

Question 9

A pendulum is suspended from the ceiling of an elevator. When the elevator accelerates upward, what happens to the period of the pendulum?

Accepted Answer

The period decreases

Question 10

A hole is drilled through the center of the Earth and you jump in. Ignoring air resistance and Earth's rotation, what happens?

Accepted Answer

You oscillate back and forth through the center, like a simple harmonic oscillator

Question 11

For a mass-spring system in simple harmonic motion, what is the expression for the total mechanical energy?

Accepted Answer

$$E = \dfrac{1}{2}mv^2$ + \dfrac{1}{2}kx^2$

Question 12

If the amplitude of a mass-spring oscillator is doubled, what happens to the maximum velocity?

Accepted Answer

It is doubled

Question 13

Which of the following is true about the period of a simple pendulum for small angles?

Accepted Answer

It depends only on the length and gravity

Question 14

A mass-spring system is oscillating on a frictionless surface. If the mass is increased, what happens to the period?

Accepted Answer

The period increases

Question 15

Which of the following is a necessary condition for a system to exhibit simple harmonic motion?

Accepted Answer

The restoring force must be proportional to the displacement

Question 16

For a simple pendulum, if the length is quadrupled, how does the period change?

Accepted Answer

It doubles

Question 17

In damped harmonic motion, what is the effect of increasing the damping coefficient $$b$$?

Accepted Answer

The oscillations die out more quickly

Question 18

A mass-spring system is oscillating with amplitude $$A. $$What is the potential energy at the maximum displacement?

Accepted Answer

$$U = \dfrac{1}{2}kA^2$

Question 19

Which of the following real-world scenarios is an example of resonance?

Accepted Answer

A child swinging higher when pushed at the right moment

Oscillations and Simple Harmonic Motion: Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards