Physics 9702 · AS & A Level · Simple harmonic oscillations

Simple harmonic oscillations — practice question

A steel ball at the lower end of a fine string makes small oscillations, as illustrated in Fig. 5.1. The displacement of the ball’s centre from equilibrium is $x$. Fig. 5.2 plots how the ball’s acceleration $a$ varies with $x$.
(a(i))[2]

Explain how Fig. 5.2 demonstrates that the ball’s oscillations are simple harmonic.

(a(ii))[3]

Determine the period $T$ for this motion.

(b(i))[2]

At time $t = 0$, the ball is at its maximum displacement and is placed in a trough of thick oil so that it lies just below the oil surface. This makes the ball’s later motion strongly damped. State what is meant by damping.

(b(ii))[3]

On Fig. 5.3, sketch a possible variation of the displacement $x$ of the ball with $t$ between $t = 0$ and $t = 2T$.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: $a$ is proportional to $x$ because the graph is a straight line through the origin

  • Full mark scheme, point by point
  • Step-by-step worked solution
  • Write your answer & get it marked instantly by AI