Find expressions for potential and kinetic energies of a particle executing simple harmonic motion.

Four different expressions for displacement of a particle executing simple harmonic motion are printed on a book: Here a = maximum displacement of the particle , v =its velocity and T = its time period. Check from dimensional analysis which of these expressions involve (s) some printing mistake.

Derive an expression for the total energy of a particle undergoing simple harmonic motion.

Show that the total mechanical energy remains constant for a particle executing simple harmonic motion.

If the displacement and the restoring force acting on a particle executing simple harmonic motion are x and F respectively, then F=-kx . Here the negative sign on the right hand side indicates that

If the displacement and the restoring force acting on a particle executing simple harmonic motion are x and F respectively, then F = -kx. Here the negative sign on the right hand side indicates that

Find the expression of potential energy of a charge conductor.

The distance between the positions of maximum potential energy and maximum kinetic energy of a particle executing SHM is