Obtain expressions for Kinetic Energy, Potential Energy and Total Energy of a particle performs linear S.H.M.

The potential energy of a particle perfonning S.H.M. is

Show that total energy of the particle performing linear S.H.M. is constant.

Ratio of kinetic energy at mean position to potential energy at A/2 of a particle performing SHM

Derive an expression for:- Kinetic energy per molecule

At the mean position, the potential energy of a particle performing S.H.M. is

Deduce the expressions for the kinetic energy and potential energy of a particle executing S.H.M. Hence obtain the expression for total energy of a particle performing S.H.M and show that the total energy is conserved. State the factors on which total energy depends.

Derive an expression for time period of a particle performing S.H.M.

Derive an expression for:- Kinetic energy per unit mass

From the differential equation of linear S.H.M. obtain expressions for acceleration, velocity and displacement of particle performing S.H.M.

Derive an expression for potential energy.