Physics 9702 · AS & A Level · Simple harmonic oscillations
Simple harmonic oscillations — practice question
A ball is kept between two fixed points A and B by two stretched springs, as shown in Fig. 3.1. The ball can oscillate along the straight line AB. The springs stay stretched, and the motion of the ball is simple harmonic. Fig. 3.2 shows how the displacement $x$ of the ball from its equilibrium position changes with time $t$.
(a(i)1)[1]
Use Fig. 3.2 to determine the amplitude of the ball’s oscillations.
(a(i)2)[2]
Use Fig. 3.2 to determine the frequency of the ball’s oscillations.
(a(ii))[2]
Show that the ball’s maximum acceleration is $5.2\,\text{m s}^{-2}$.
(b)[2]
Use your answers in (a) to plot, on the axes of Fig. 3.3, the relationship between displacement $x$ and the acceleration $a$ of the ball.
(c)[3]
Calculate the displacement of the ball for which its kinetic energy is equal to one half of the maximum kinetic energy.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “amplitude of oscillation $=1.7\,\text{cm}$” …