Question

derive an expression for total energy of a particle executing SHM​

Answer 1

The sum of kinetic energy and potential energy is the total energy of the particles executing simple harmonic motion.

kinetic energy-the energy possess by the particle due to its motion is called kinetic energy.

kinetic energy of the particle executing simple harmonic motion=mv²/2

=1/2m(wAcoswt)²

=1/2mw²A²cos²wt

1/2mw²A²(1-sin²wt)

1/2mw²(A²-À²sin²wt)

=1/2mw²(A²-y²)

this is the required expression of the kinetic energy of the particle executing SHM.