A mass is suspended vertically from a fixed point by means of a spring, as illustrated in Fig. 4.1. [Figure 4.1] The mass is oscillating vertically. The variation with displacement x of the acceleration a of the mass is shown in Fig. 4.2. [Figure 4.2]

1. (a)(i)State what is meant by the displacement of the mass on the spring.[1]
2. (a)(ii)Suggest how Fig. 4.2 shows that the mass is not performing simple harmonic motion.[1]
3. (b)(i)The amplitude of oscillation of the mass may be changed. State the maximum amplitude x₀ for which the oscillations are simple harmonic.[1]
4. (b)(ii)For the simple harmonic oscillations of the mass, use Fig. 4.2 to determine the frequency of the oscillations.[3]
5. (c)The maximum speed of the mass when oscillating with simple harmonic motion of amplitude x₀ is v₀. On Fig. 4.3, show the variation with displacement x of the velocity v of the mass for displacements from +x₀ to –x₀. [Figure 4.3][2]

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