State two conditions necessary for a mass to be undergoing simple harmonic motion.

1. (a)State two conditions necessary for a mass to be undergoing simple harmonic motion.[2]
2. (b)(i)1.A trolley of mass 950g is held on a horizontal surface by means of two springs attached to fixed points P and Q, as shown in Fig. 4.1. The springs, each having a spring constant k of 230 Nm⁻¹, are always extended. The trolley is displaced along the line of the springs and then released. The variation with time t of the displacement x of the trolley is shown in Fig. 4.2. State and explain whether the oscillations of the trolley are heavily damped, critically damped or lightly damped.[3]
3. (b)(i)2.Suggest the cause of the damping.[3]
4. (b)(ii)1.The acceleration a of the trolley of mass m may be assumed to be given by the expression a = – (2k/m)x. Calculate the angular frequency ω of the oscillations of the trolley.[3]
5. (b)(ii)2.Determine the time t₁ shown on Fig. 4.2.[2]

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