Simple Harmonic Motion (CIE A Level Physics)

A pendulum consists of a bob (small plastic sphere) attached to the end of a piece of wire. The other end of the wire is attached to a fixed point. The bob oscillates with small oscillations about its equilibrium position, as shown in Fig. 1.1.

The length L of the pendulum, measured from the fixed point to the centre of the bob, is 1.56 m.

The acceleration a of the bob varies with its displacement x from the equilibrium position as shown in Fig. 1.2.

State how Fig. 1.2 shows that the motion of the pendulum is simple harmonic. 

Use Fig. 1.2 from (a) to calculate the angular frequency ω of the oscillations.

The angular frequency ω is related to the length L of the pendulum by 

where k is a constant. 

Use your answer from (b) to determine k. Give a unit for your answer.

Whilst the pendulum is oscillating, the length of the string is decreased in such a way that the total energy of the oscillations remains constant. 

Suggest and explain the qualitative effect of this change on the amplitude of the oscillations.

An object is suspended from a spring that is attached to a fixed point as shown in Fig. 1.1.

The object oscillates vertically with simple harmonic motion about its vertical position. 

State the defining equation for simple harmonic motion. Identify the meaning of each of the symbols used to represent Physical quantities. 

The variation with displacement x from the equilibrium position of the velocity v of the object is shown in Fig. 1.2.

The oscillations of the object are now heavily damped.