Question

Show that when a body is suspended from a spring and is pulled down a little and released, it executes S.H.M. Also find an expression for its time period. Does it depend on acceleration due to gravity?

Answer 1

In simple harmonic motion; when the particle is displaced then the potential energy is obtained in the form of negative value of the work done opposite to the restoring force F = -ky. Hence, increase in the potential energy of the particle;

∆U = -F dy

Hence, potential energy in displacing the particle to a distance y from the mean position is;

Average potential energy per unit time period

It is clear from Eqs.(1) and (2) that the value of average kinetic energy and average potential energy per unit time period is \(\frac{1}{4}\)ka².