A simple pendulum is set into simple harmonic motion (SHM). Which of the following equations best describes its motion?

A. F = ma

B. a = w^2 x

C. v = w x

D. F = kx

Which of the following best describes the energy transitions in a simple harmonic oscillator?

A. Kinetic energy is maximum at the equilibrium position.

B. Potential energy is maximum at the equilibrium position.

C. Both kinetic and potential energy are maximum at the equilibrium position.

D. Neither kinetic nor potential energy is maximum at the equilibrium position.

A system undergoing damped harmonic motion eventually comes to a stop. Which type of damping is this?

A. Overdamping

B. Underdamping

C. Critical damping

D. No damping

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

A. A child pushing a swing at regular intervals.

B. A guitar string vibrating when plucked.

C. A glass shattering when a singer hits a particular note.

D. A ball bouncing on the ground.

In a simple harmonic oscillator, when is the potential energy maximum?

A. At the equilibrium position

B. At the maximum displacement

C. Halfway between the equilibrium position and maximum displacement

D. Potential energy remains constant throughout the motion

a) Define Simple Harmonic Motion (SHM) and state its defining equation. [2]

b) A body is undergoing SHM with a maximum displacement of 0.5 m and a period of 3 seconds. Calculate its angular frequency and maximum velocity. [3]

a) Describe the energy transitions between potential and kinetic energy in a simple pendulum undergoing SHM. [3]

b) A pendulum has a length of 1.2 m and is displaced by 10° from the vertical. Calculate the potential energy at this position if the bob has a mass of 0.5 kg. [2]

a) Define overdamping, underdamping, and critical damping in the context of oscillations. Provide a real-world example for each. [3]

b) Explain why bridges are designed to avoid resonance. [2]

a) What is the phase difference between two oscillating particles when one is at its maximum positive displacement and the other is at its maximum negative displacement? [2]

b) A mass-spring system oscillates with a frequency of 5 Hz. If the mass is doubled while keeping the spring constant unchanged, what will be the new frequency of oscillation? [3]

c) How does the amplitude of an oscillating system affect its period? [2]

a) Define resonance in the context of oscillations. [2]

b) A tuning fork is struck and produces a sound with a frequency of 440 Hz. If another tuning fork nearby starts to vibrate at the same frequency without being struck, explain the phenomenon. [3]

c) Why is it dangerous for soldiers to march in step across a bridge? [3]

Which of the following is NOT a characteristic of simple harmonic motion (SHM)?

A. The restoring force is directly proportional to the displacement.

B. The motion is periodic.

C. The acceleration is maximum at the equilibrium position.

D. The velocity is zero at maximum displacement.

A tuning fork is struck and produces a sound. Another identical tuning fork nearby starts to vibrate. What phenomenon is this an example of?

A. Damping

B. Resonance

C. Reflection

D. Refraction

In a damped harmonic oscillator, if the damping force just prevents oscillation, what type of damping is it?

A. Overdamping

B. Underdamping

C. Critical damping

D. No damping

For a mass-spring system in SHM, if the mass is doubled while keeping the spring constant unchanged, what happens to the period of oscillation?

A. It remains unchanged.

B. It becomes half.

C. It becomes double.

D. It becomes four times.

Which of the following scenarios is an example of underdamping in SHM?

A. A car's shock absorber comes to rest quickly without oscillating.

B. A door closes slowly without oscillating.

C. A pendulum comes to rest after a few oscillations.

D. A ball bounces several times before coming to rest.

a) Differentiate between free oscillations and forced oscillations. [3]

b) A child pushes a swing at regular intervals. What condition must be met for the swing to reach its maximum height? [2]

c) Describe the effect of damping on the amplitude of a forced oscillation as the frequency of the external force approaches the system's natural frequency. [3]

a) What is the relationship between the angular frequency and the period of an oscillating system? [2]

b) A system has an angular frequency of 10 rad/s. Calculate its period. [3]

c) How does increasing the mass of a pendulum affect its angular frequency and period? [3]

a) What is meant by the term 'natural frequency' in the context of oscillations? [2]

b) A pendulum is set into oscillation and its displacement from the mean position is observed to decrease over time. What is causing this decrease? [2]

c) If the length of a simple pendulum is quadrupled, by what factor does its period change? [3]

d) A car's suspension system can be modelled as a damped harmonic oscillator. Why is it undesirable for the suspension system to undergo resonance? [3]

a) Describe the energy changes that occur during one complete cycle of simple harmonic motion. [3]

b) A mass-spring system has a spring constant of 500 N/m. If a 2 kg mass is attached to the spring, calculate the angular frequency of the system. [3]

c) How does the amplitude of a damped oscillator change over time? [2]

d) In the context of oscillations, what is meant by 'phase difference'? [2]

a) What is the difference between 'overdamping', 'underdamping', and 'critical damping'? [3]

b) A system undergoing simple harmonic motion has a maximum velocity of 5 m/s and a maximum displacement of 0.5 m. Calculate its angular frequency. [3]

c) How does the frequency of a forced oscillator compare to its natural frequency at resonance? [2]

d) Why do buildings in earthquake-prone areas have dampers installed? [2]