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]