A trolley on a smooth surface is attached by springs to fixed blocks as shown in Fig. 4.1. The trolley oscillates horizontally about its equilibrium position with an amplitude of 12 cm. Fig. 4.2 shows the variation of the acceleration a of the trolley with displacement x from its equilibrium position. Friction between the trolley and the surface can be assumed to be negligible. [Figure 4.1] [Figure 4.2]

1. (a)Describe the features of the line in Fig. 4.2 that demonstrate that the motion of the trolley is simple harmonic.[2]
2. (b)Use Fig. 4.2 to determine the period T of the oscillations of the trolley.[3]
3. (c)(i)On the line of the graph of Fig. 4.2, label with the letter P one point where the kinetic energy of the trolley is zero.[1]
4. (c)(ii)On the line of the graph of Fig. 4.2, label with the letter Q an approximate position of one point where the kinetic energy of the trolley is equal to the potential energy stored in the springs.[1]

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