Question

For a particle executing shm the kinetic enrgyis kcos^2wt the maximum value of potential energy is (given potential energy at mean position is zero)

Answer 1

answer : maximum potential energy = k

explanation : we know, in Simple harmonic motion, total energy of the particle is constant at all instant which has totally kinetic energy when the particle passing through mean position and is totally potential energy when the particle passing through extreme position.

e.g., total energy at mean position = kinetic energy { it is maximum kinetic energy}

and total energy at extreme position = potential energy { it is maximum potential energy }

for a particle executing SHM the kinetic energy is $K.E=kcos^2\omega t$

so, maximum kinetic energy = K , because maximum value of cos²$\omega t$ is 1

so, total energy at mean position = K

and total energy at extreme position = K = maximum potential energy

hence, maximum potential energy = K