SHM Solving Problems

A particle oscillates with undamped simple harmonic motion. Which one of the following statements about the acceleration of the oscillating particle is true?

• It is least when the speed is greatest

• It is always in the opposite direction to its velocity

• It is proportional to the frequency

• It decreases as the potential energy increases

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

• The acceleration is always away from O

• The acceleration and velocity are always in opposite directions

• The acceleration and the displacement from O are always in the same direction

• The graph of acceleration against displacement is a straight line

A simple pendulum and a mass-spring system are taken to the Moon, where the gravitational field strength is less than on Earth.

Which line, A to D, correctly describes the change, if any, in the period when compared with its value on Earth?

• A

• B

• C

• D

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

• the time period

• the total energy

• the maximum velocity

• the maximum acceleration

Which one of the following statements concerning the acceleration of an object moving with simple harmonic motion is correct?

• It is constant

• It is at a maximum when the object moves through the centre of the oscillation

• It is zero when the object moves through the centre of the oscillation

• It is zero when the object is at the extremity of the oscillation

Which one of the following gives the phase difference between the particle velocity and the particle displacement in simple harmonic motion?

•  $\frac{\pi}{4}$  

•  $\frac{\pi}{2}$  

•  $\frac{3\pi}{4}$  

•  $2\pi$  

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

The displacement (in mm) of the vibrating cone of a large loudspeaker can be represented by the equation x = 10 cos (150t), where t is the time in s. Which line, A to D, in the table gives the amplitude and frequency of the vibrations

• A

• B

• C

• D

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?

• $0.025\ m\cdot s^{-2}$

• $0.99\ m\cdot s^{-2}$

• $2.5\ m\cdot s^{-2}$

• $9.8\ m\cdot s^{-2}$

When a mass suspended on a spring is displaced, the system oscillates with simple harmonic motion.

Which one of the following statements regarding the energy of the system is incorrect?

• The potential energy has a minimum value when the spring is fully compressed or fully extended

• The kinetic energy has a maximum value at the equilibrium position

• The sum of the kinetic and potential energies at any time is constant

• The potential energy has a maximum value when the mass is at rest