Question

When a particle oscillates simple harmonically, its kinetic energy varies periodically. If frequency of the particle is n, then the frequency of the kinetic energy is ______.

Options

• 4n

• n 

• 2n

• n/2

Answer 1

When a particle oscillates simple harmonically, its kinetic energy varies periodically. If frequency of the particle is n, then the frequency of the kinetic energy is 2n.

Explanation:

PE = `1/2"m"omega^2x^2`

= `1/2"m"omega^2(x_0^2sin^2omega"t")`

= `1/2"m"omega^2x_0^2((1-cos2omegat)/2)`

= `1/4"m"omega^2x_0^2-1/4"m"omega^2x_0^2cos2omega"t"`

frequency of above equation i.e. frequency of P.E. is 2ω or 2n.