A light, elastic string, of natural length 2m and modulus of elasticity 40N, has one end attached to a ceiling at the point O. A particle of mass 0.5 kg is attached to the other end of the string. And the system is allowed to rest in equilibrium with the string taut.

a. Find the extension in the string. The particle is then pulled down a further 0.75m and released.

b. Find the shortest distance between the particle and O in the subsequent motion.

c. Show that while the string is taut the particle performs simple harmonic motion.