Physics 9702 · AS & A Level · Damped and forced oscillations, resonance
Damped and forced oscillations, resonance — practice question
A trolley moving along a track is connected by springs to fixed blocks $X$ and $Y$, as shown in Fig. 4.1. The track has many tiny holes through which air is driven vertically upward. This makes the trolley ride on a cushion of air instead of touching the track directly.
The trolley is displaced to one side of its equilibrium position and then released, so that it first oscillates with simple harmonic motion. After a short time, the air blower is turned off. Fig. 4.2 shows how the distance $L$ of the trolley from block $X$ varies with time $t$.
(a(i))[1]
Use Fig. 4.2 to find the initial amplitude of the oscillations.
(a(ii))[2]
Use Fig. 4.2 to find the angular frequency $\omega$ of the oscillations.
(a(iii))[2]
Use Fig. 4.2 to find the maximum speed $v_0$, in $\text{cm s}^{-1}$, of the oscillating trolley.
(b)[3]
Other than the quantities in (a), describe what can be inferred from Fig. 4.2 about the trolley’s motion between time $t = 0$ and time $t = 24\,\text{s}$. No calculations are needed.
(c)[3]
On Fig. 4.3, sketch how the velocity $v$ of the trolley varies with $L$ for its 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: “Amplitude $5.0\,\text{cm}$” …