A trolley on a track is attached by springs to fixed blocks X and Y, as shown in [Figure 4.1]. The track contains many small holes through which air is blown vertically upwards. This results in the trolley resting on a cushion of air rather than being in direct contact with the track. The trolley is pulled to one side of its equilibrium position and then released so that it oscillates initially with simple harmonic motion. After a short time, the air blower is switched off. The variation with time t of the distance L of the trolley from block X is shown in [Figure 4.2].

1. (a)(i)Use [Figure 4.2] to determine: the initial amplitude of the oscillations[1]
2. (a)(ii)the angular frequency ω of the oscillations[2]
3. (a)(iii)the maximum speed v₀, in cm s⁻¹, of the oscillating trolley.[2]
4. (b)Apart from the quantities in (a), describe what may be deduced from [Figure 4.2] about the motion of the trolley between time t = 0 and time t = 24 s. No calculations are required.[3]
5. (c)On [Figure 4.3], sketch the variation with L of the velocity v of the trolley for its first complete oscillation.[3]

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