P.3.6.1.3 Simple Harmonic Systems

Two pendulums A and B oscillate with simple harmonic motion. The time period of A is 2.00 s and the time period of B is 1.98 s.

A and B are released in phase.

What is the number of oscillations of A before A and B are next in phase?

• 49

• 50

• 99

• 100

The frequency of oscillation of a vertical spring is f when the mass hanging from the spring is m.

What is the relationship between f and m?

• f ∝ m^–½

• f ∝ m^–2

• f ∝ m^½

• f ∝ m²

Which graph shows how the gravitational potential energy E_p of a simple pendulum varies with displacement s from the equilibrium position?

• A

• B

• C

• D

Which graph best shows how the kinetic energy of a simple pendulum varies with displacement from the equilibrium position?

• A

• B

• C

• D

The graph shows how the displacement of a particle performing simple harmonic motion varies with time.

Which statement is not correct?

• The speed of the particle is a maximum at time T/4

• The potential energy of the particle is zero at time 3T/4

• The acceleration of the particle is a maximum at time T/2

• The restoring force acting on the particle is zero at time T

A simple pendulum and a mass−spring system perform simple harmonic oscillations on Earth with the same period T. Both systems are moved to a region where the gravitational field strength is four times that at the surface of Earth.

What is the period of each system when oscillating at this new location?

• A

• B

• C

• D

A simple pendulum and a mass-spring system have the same oscillation frequency f at the surface of the Earth. The pendulum and the mass-spring system are taken down a mine where the acceleration due to gravity is less than at the surface. What is the change in the frequency of the simple pendulum and the change in the frequency of the mass-spring system?

• A

• B

• C

• D

The graph shows how velocity changes with time for a simple pendulum moving with simple harmonic motion.

Which one of the following statements related to the motion of the pendulum is incorrect?

• The acceleration is a minimum at T/4

• The acceleration is a maximum at T/2

• The kinetic energy is a maximum at T/2

• The restoring force is a minimum at 3T/4

A mass hanging on the end of a spring undergoes vertical simple harmonic motion. At which point(s) is the magnitude of the resultant force on the mass a minimum?

• at both the top and bottom of the oscillation

• only at the top of the oscillation

• only at the bottom of the oscillation

• at the centre of the oscillation

A simple pendulum has a time period of 1.42 s on Earth. The gravitational field strength at the surface of Mars is 0.37 times that at the surface of the Earth.

What is the time period of the pendulum on Mars?

• 0.53 s

• 0.86 s

• 2.33 s

• 3.84 s