A block of mass m is attached to a horizontal spring fixed at one end. The block is free to oscillate on a frictionless surface about its equilibrium position x=0.
(i) State the mathematical form of the restoring force exerted by the spring when the block is displaced by a distance x from equilibrium.
(ii) Taking the positive direction to be towards the right, explain with the help of signs the direction of the restoring force and the resulting acceleration when the block is at (a) x=+0.05m and (b) x=−0.05m.
(iii) Using your explanation in part (ii), justify why the acceleration of the block is always directed towards the equilibrium position irrespective of whether the displacement is positive or negative.
(iv) How does this behaviour satisfy the essential condition for simple harmonic motion?