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]

A system is subjected to forced vibrations at a frequency equal to its natural frequency. What phenomenon is observed?

A. Damping

B. Resonance

C. Overdamping

D. Underdamping

In an underdamped harmonic oscillator, which of the following statements is true?

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.

Which of the following best describes critical damping?

A. The damping is so strong that the system returns to its equilibrium position without any oscillations.

B. The system oscillates with decreasing amplitude.

C. The system returns to equilibrium in the shortest time without oscillating.

D. The system oscillates with constant amplitude.

In simple harmonic motion, the phase difference between the displacement and velocity of the oscillating body is:

A. 0°

B. 90°

C. 180°

D. 270°

A body undergoing simple harmonic motion has a maximum displacement of 5 cm and an angular frequency of 10 rad/s. What is the maximum velocity of the body?

A. 0.5 m/s

B. 5 m/s

C. 50 m/s

D. 500 m/s

a) What is meant by 'overdamping' in simple harmonic motion? [2]

b) Explain the significance of the phase difference between the displacement and acceleration in simple harmonic motion. [3]

c) How does the amplitude of an oscillating system change with increasing damping? [2]

a) Define 'resonance' in the context of simple harmonic motion. [2]

b) A tuning fork is made to vibrate near another identical tuning fork at rest. After some time, the second tuning fork starts to vibrate. Explain this phenomenon. [3]

c) How does the phenomenon of resonance relate to the destruction of bridges by marching soldiers? [2]

a) Describe the principle of conservation of energy in the context of a simple harmonic oscillator. [3]

b) A pendulum is set into simple harmonic motion. At its maximum displacement, its potential energy is 5 J. Calculate its kinetic energy when it passes through its equilibrium position. [3]

c) What is the significance of the 'amplitude' in simple harmonic motion? [2]

d) How does the energy of a damped harmonic oscillator change over time? [2]

a) Define 'critical damping' and explain its significance in practical applications. [3]

b) A body in simple harmonic motion has a period of 2 seconds. Calculate its frequency. [2]

c) How does the frequency of a simple harmonic oscillator relate to its energy? [3]

d) Describe the phenomenon of 'beats' and how it relates to the Doppler effect. [2]

a) What is meant by 'forced vibrations' in the context of resonance? [2]

b) Explain how resonance can be both beneficial and detrimental in real-world applications. [3]

c) A tuning fork has a natural frequency of 440 Hz. If it is exposed to a range of frequencies, at which frequency will it resonate? [2]

d) Describe the difference between 'transverse' and 'longitudinal' waves and give an example of each. [3]