A body is undergoing simple harmonic motion (SHM). Which of the following relationships correctly describes the acceleration a of the body in terms of its displacement x from the equilibrium position and the angular frequency ω?

A. a = ω^2 x

B. a = ω x

C. a = x/ω^2

D. a = ω/x

Which of the following scenarios best describes overdamping in a damped harmonic oscillator?

A. The system returns to equilibrium without oscillating.

B. The system oscillates with decreasing amplitude.

C. The system oscillates with constant amplitude.

D. The system oscillates with increasing amplitude.

A pendulum is set into simple harmonic motion. At which position is the potential energy of the pendulum maximum?

A. At the equilibrium position

B. At the maximum displacement

C. Halfway between the equilibrium and maximum displacement

D. At one-fourth of the maximum displacement

In simple harmonic motion, when is the kinetic energy of the oscillating body maximum?

A. At the equilibrium position

B. At the maximum displacement

C. Halfway between the equilibrium and maximum displacement

D. At one-fourth of the maximum displacement

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

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

B. The motion is periodic.

C. The acceleration is constant.

D. The velocity is zero at maximum displacement.

a) Define Simple Harmonic Motion (SHM) and state the conditions required for a motion to be considered as SHM. [2]

b) A particle is undergoing SHM with a maximum displacement of 0.05 m and a period of 3 seconds. Calculate its maximum velocity. [3]

a) Describe the energy transitions that occur in a simple pendulum undergoing SHM. [2]

b) If a pendulum has a maximum potential energy of 5 J at its extreme positions, calculate its kinetic energy when it is halfway to its maximum displacement. [3]

a) Define damping in the context of SHM and list the three types of damping mentioned in the subtopic. [2]

b) A system undergoing SHM is observed to return to its equilibrium position without oscillating. Identify the type of damping exhibited by the system and explain your choice. [3]

a) Define damping and list its types in the context of simple harmonic motion. [2]

b) A car's shock absorber is designed to critically damp the car's oscillations. Explain the significance of this design choice. [3]

c) How does the Doppler effect relate to simple harmonic motion, especially in the context of sound waves? [2]

a) Describe the relationship between displacement, velocity, and acceleration in simple harmonic motion. [3]

b) A body is undergoing simple harmonic motion with a frequency of 3 Hz. Calculate the time period of the motion. [2]

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