Question 1

Which of the following best describes the condition for an object to exhibit simple harmonic motion (SHM)?

Accepted Answer

The restoring force is proportional to the displacement and acts in the opposite direction.

Question 2

A mass $$m$$ attached to a spring with spring constant $$k$$ oscillates with a period $$T. $$What is the correct expression for the period $$T of $$the oscillation?

Accepted Answer

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

Question 3

If the spring constant $$k of a $$mass-spring system is quadrupled while the mass $$m$$ remains the same, what happens to the period $$T of $$oscillation?

Accepted Answer

The period is halved.

Question 4

A glider of mass $$0.50\ \mathrm{kg} is $$attached to a spring with $$k = 200\ \mathrm{N/m}. If it is $$released from rest at $$x = A$$, how much time does it take to reach $$x = 0$$ for the first time?

Accepted Answer

$$T/4$$

Question 5

The time period of a simple pendulum depends on which of the following parameters?

Accepted Answer

Length of the pendulum and gravitational acceleration

Question 6

What is the correct formula for the period $$T of a $$simple pendulum of length $$l in a $$gravitational field $$g$$?

Accepted Answer

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

Question 7

If you take a simple pendulum from Earth to the Moon (where $$g_{moon} \approx 1/6\ g_{earth}$$), what happens to its period?

Accepted Answer

The period increases by a factor of $$\sqrt{6}.$$

Question 8

Which force acts as the restoring force for a simple pendulum undergoing small oscillations?

Accepted Answer

$$mg \sin 	heta$$

Question 9

A Foucault pendulum is used to demonstrate which physical phenomenon?

Accepted Answer

The rotation of the Earth

Question 10

A child on a swing is pushed by their parent. To maximize the amplitude of the swing, the parent should push:

Accepted Answer

At the natural frequency of the swing

Question 11

Which of the following best describes resonance in a physical system?

Accepted Answer

A large amplitude oscillation occurs when the driving frequency matches the natural frequency.

Question 12

What is the effect of increasing the damping force on a driven oscillator?

Accepted Answer

The amplitude of resonance decreases and the resonance peak broadens.

Question 13

Which equation describes the position $$x(t) of an $$object in simple harmonic motion with amplitude $$A$$ and angular frequency $$\omega$$?

Accepted Answer

$$x(t) = A \cos(\omega t + \phi)$$

Question 14

A mass-spring system oscillates with $$k = 20\ \mathrm{N/m}$$ and $$m = 0.30\ \mathrm{kg}. If $$you want to double the frequency, what should the new value of $$k be ($$with $$m$$ unchanged)?

Accepted Answer

$$k = 80\ \mathrm{N/m}$$

Question 15

Which of the following is a real-world example of resonance causing structural failure?

Accepted Answer

The collapse of the Tacoma Narrows Bridge

Question 16

In a damped oscillator, what happens to the total mechanical energy over time?

Accepted Answer

It decreases due to energy dissipation (e.g., friction or air resistance).

Question 17

Which of the following best explains why the mass of the bob does not affect the period of a simple pendulum?

Accepted Answer

Both the restoring force and inertia are proportional to mass, so mass cancels out.

Question 18

A vibrating rod and a child on a swing both demonstrate which physical principle?

Accepted Answer

Resonance due to periodic driving at the natural frequency

Question 19

For a damped oscillator, which of the following best describes the motion?

Accepted Answer

The amplitude of oscillation decreases over time.

Periodic Motion: Simple Harmonic Motion, Pendulums, Damping, and Resonance

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