A spring stretches by 0.3 m when a mass of 1.0 kg is hung from it. The spring is stretched by a further 0.2 m from this equilibrium point and released so that the mass oscillates up and down with simple harmonic motion. (a) Write down the relationship between the restoring force F and displacement x for a body in simple harmonic motion. (1 Mark) (b) Calculate the period of the simple harmonic motion. (2 Marks) (c) Sketch a graph of the displacement of the mass as a function of time, for the first three cycles of the periodic motion, indicating the magnitude of both the period and amplitude of the oscillation. Indicate on your sketch positions within the period motion where: (i) The speed of the mass is a maximum (label these vmax) (ii) The acceleration of the mass has its maximum magnitude (label these amax) (4 Marks) (d) Calculate the maximum speed and maximum magnitude of the acceleration of the mass. (2 Marks)