P.3.6.1.2 Simple Harmonic Motion (SHM)

The graph shows the variation of displacement d with time t for a particle moving with simple harmonic motion of period T.

Which graph shows the variation of kinetic energy E_k of the particle with time?

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A body performs simple harmonic motion.

What is the phase difference between the variation of displacement with time and the variation of acceleration with time for the body?

• 0

• π/4 rad

• π/2 rad

• π rad

An object of mass 0.15 kg performs simple harmonic motion. It oscillates with amplitude 55 mm and frequency 0.80 Hz

What is the maximum value of its kinetic energy?

• 5.7 × 10^–3 J

• 11 × 10^–3 J

• 0.57 J

• 11 J

Which graph shows how the velocity v of a body moving with simple harmonic motion varies with its displacement x?

• A

• B

• C

• D

The frequency of a body moving with simple harmonic motion is doubled. If the amplitude remains the same which of the following is also doubled?

• The time period.

• The total energy.

• The maximum velocity.

• The maximum acceleration.

A particle oscillates with undamped simple harmonic motion.

The acceleration of the particle

• is always in the opposite direction to its velocity.

• decreases as the potential energy increases.

• is proportional to the frequency.

• is least when the speed is greatest.

Which one of the following statements is true when an object performs simple harmonic motion about a central point?

• The acceleration is always directed away from the central point.

• The acceleration and velocity are always 180° out of phase.

• The velocity and displacement are always in the same direction.

• Acceleration and displacement are always 180° out of phase.

For a body performing simple harmonic motion, which one of the following statements is correct?

• The maximum kinetic energy is directly proportional to the frequency.

• The time for one oscillation is directly proportional to the frequency.

• The speed at any instant is directly proportional to the displacement.

• The maximum acceleration is directly proportional to the amplitude.

A particle of mass 5.0 × 10^–3 kg, moving with simple harmonic motion of amplitude 0.15 m, takes 47 s to make 50 oscillations.

What is the maximum kinetic energy of the particle?

• 2.0 × 10^–3 J

• 2.5 × 10^–3 J

• 3.9 × 10^–3 J

• 5.0 × 10^–3 J

Which line, A to D, in the table gives the amplitude and frequency of a body performing simple harmonic motion whose displacement x at time t is given by the equation x = P cos Qt?

• A

• B

• C

• D