Simple harmonic motion equations

A particle performs simple harmonic motion with a time period of 1.4 s and an amplitude of 12 mm.

What is the maximum speed of the particle?

• 8.6 mm s⁻¹

• 27 mm s⁻¹

• 54 mm s⁻¹

• 110 mm s⁻¹

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.

Which one of the following graphs shows how the acceleration, a, of a body moving with simple harmonic motion varies with its displacement, x?

• A

• B

• C

• D

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?

• Amplitude = P/2, Frequency = Q/2π

• Amplitude = P, Frequency = 2πQ

• Amplitude = P, Frequency = Q/2π

• Amplitude = 2P, Frequency = Q/2π

The graph shows the variation in displacement with time for an object moving with simple harmonic motion. What is the maximum acceleration of the object?

• 0.025 m s^–2

• 0.99 m s^–2

• 2.5 m s^–2

• 9.8 m s^–2

A body moves with simple harmonic motion of amplitude 0.90 m and period 8.9 s. What is the speed of the body when its displacement is 0.70 m?

• 0.11 m s^–1

• 0.22 m s^–1

• 0.40 m s^–1

• 0.80 m s^–1