Physics 9702 · AS & A Level · Simple harmonic oscillations

Simple harmonic oscillations — practice question

A mass is hanging vertically from a fixed point by a spring, as shown in Fig. 4.1. The mass moves up and down. Fig. 4.2 shows how the acceleration $a$ changes with displacement $x$ of the mass.
(a(i))[1]

State what is meant by the displacement of the mass on the spring.

(a(ii))[1]

Suggest how Fig. 4.2 shows that the mass is not performing simple harmonic motion.

(b(i))[1]

The amplitude of oscillation of the mass may be varied. State the maximum amplitude $x_0$ for which the oscillations are simple harmonic.

(b(ii))[3]

For the simple harmonic oscillations of the mass, use Fig. 4.2 to find the frequency of the oscillations.

(c)[2]

The greatest speed of the mass when it is oscillating with simple harmonic motion of amplitude $x_0$ is $v_0$. In Fig. 4.3, show the variation with displacement $x$ of the velocity $v$ of the mass for displacements from $+x_0$ to $-x_0$.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: separation from a reference point in a specified direction

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