18 Energy in Oscillations

Which one of the following statements is not true for a body vibrating in simple harmonic motion when damping is present?

• The damping force is always in the opposite direction to the velocity.

• The damping force is always in the opposite direction to the acceleration.

• The presence of damping gradually reduces the maximum potential energy of the system.

• The presence of damping gradually reduces the maximum kinetic energy of the system.

A body executes simple harmonic motion. Which one of the graphs, A to D, best shows the relationship between the kinetic energy, E_k, of the body and its distance from the centre of oscillation?

• A

• B

• C

• D

A body executes simple harmonic motion. The potential energy, the kinetic energy and total energy are measured as a function of displacement x. Which of the following statements is true?

• Kinetic energy is maximum when x = 0

• Total energy is zero, when x = 0

• Kinetic energy is maximum when x is maximum

• Potential energy is maximum when x = 0

The diagram shows a string XY supporting a heavy pendulum P and four pendulums A, B, C and D of smaller mass.

Pendulum P is set in oscillation perpendicular to the plane of the diagram.

Which one of the pendulums, A to D, then oscillates with the largest amplitude?

• A

• B

• C

• D

A periodic force is applied to a lightly-damped object causing the object to oscillate.

The graph shows how the amplitude A of the oscillations varies with the frequency f of the periodic force.

Which one of the following statements best describes how the shape of the curve would differ if the damping had been greater?

• the curve would be lower at all frequencies

• the curve would be higher at all frequencies

• the curve would be unchanged except at frequencies above the resonant frequency where it would be lowe

• the curve would be unchanged except at frequencies above the resonant frequency where it would be higher

Which one of the following statements always applies to a damping force acting on a vibrating system?

• It is in the same direction as the acceleration.

• It is in the same direction as the displacement.

• It is in the opposite direction to the velocity.

• It is proportional to the displacement.

What is maximum value of kinetic energy in SHM

• ½mω²A²

• mω²A²

• ½mω²x²

• A_max

Diagram below shows a graph of an oscillation system experiences damping.

Which of the following quantity does not change?

• Size of oscillation

• Period of oscillation

• Energy of oscillation

• Amplitude of oscillation

The variation with frequency f of the amplitude x_o of the forced oscillations of a machine is as shown. Which of the following statement is false?

• The resonant frequency of the system is 12 Hz

• The amplitude of the drive is 2cm

• Increased damping reduces the sharpness of the resonance peak

• Damping decreases the maximum amplitude of the oscillations

Complete the following sentence: Resonance occurs in harmonic motion when

• the system is over damped.

• the system is critically damped.

• the energy in the system is a minimum.

• the driving frequency is the same as the natural frequency of the system.