Question

Q) . Using the expression for the kinetic energy and potential energy of a particle in simple harmonic motion at any position, show that
i) at the mean position, total energy = kinetic energy
ii) at an extreme position total energy = potential energy.​

Answer 1

Answer:

I) At the mean position, the total energy in simple harmonic motion is purely kinetic and at the extreme position, the total energy in simple harmonic motion is purely potential energy. At other positions, kinetic and potential energies are interconvertible and their sum is equal to 1/2 k a2.

ii) The total energy of a particle is purely potential at both extreme points of its motion because, at the extreme position, the velocity of the particle executing SHM will be zero. So, the kinetic energy of the particle becomes zero at extreme positions and the whole energy is in the form of potential energy.