Physics 9702 · AS & A Level · Damped and forced oscillations, resonance
Damped and forced oscillations, resonance — practice question
A trolley moving along a track is linked by springs to fixed blocks $X$ and $Y$, as shown in Fig. 4.1. The track has many tiny holes through which air is blown vertically upwards. This means the trolley rests on a cushion of air instead of touching the track directly.
The trolley is drawn to one side of its equilibrium position and then released, so that at first it oscillates with simple harmonic motion. After a short time, the air blower is turned off. The way the distance $L$ of the trolley from block $X$ changes with time $t$ is shown in Fig. 4.2.
(a(i))[1]
From Fig. 4.2, determine the initial amplitude of the oscillations.
(a(ii))[2]
From Fig. 4.2, determine the angular frequency $\omega$ of the oscillations.
(a(iii))[2]
Use Fig. 4.2 to determine the maximum speed $v_0$, in $\text{cm s}^{-1}$, of the oscillating trolley.
(b)[3]
Apart from the quantities in (a), what can be inferred from Fig. 4.2 about the motion of the trolley between time $t = 0$ and time $t = 24\,\text{s}$? No calculations are needed.
(c)[3]
On Fig. 4.3, sketch how the velocity $v$ varies with $L$ for the trolley's first complete oscillation.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “5.0\,\text{cm} for the amplitude” …