Physics 9702 · AS & A Level · Simple harmonic oscillations
Simple harmonic oscillations — practice question
A ball is trapped between two fixed points A and B by means of two stretched springs, as illustrated in Fig. 3.1. It is free to move to and fro along the straight line AB. Because the springs stay stretched, the ball undergoes simple harmonic motion. Fig. 3.2 shows how the displacement $x$ of the ball from its equilibrium position varies 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 maximum acceleration of the ball is $5.2\,\text{m s}^{-2}$.
(b)[2]
Use your answers in (a) to plot, on the axes of Fig. 3.3, how the acceleration $a$ of the ball varies with displacement $x$.
(c)[3]
Calculate the displacement of the ball for which its kinetic energy equals one half of its greatest 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 is $1.7\,\text{cm}$” …