If the frequency of a simple harmonic motion be n then find the frequency of its kinetic energy.

Explanation

If the particle executing the simple harmonic motion, then
displacement, `x=Asin(omegat+theta)`
= `Asin(2pint+theta)" "[becausen=omega/(2pi)]`
`therefore" "` Velocity, `v=(dx)/(dt)=Aomegacos(omegat+theta)` So, the kinetic energy, if the particle has a mass m, is
`K=1/2mv^(2)=1/2mA^(2)omega^(2)cos^(2)(omegat+theta)`
= `1/4mA^(2)omega^(2)" "[1+cos2(omegat+theta)]`
= `1/4mA^(2)omega^(2)+1/4mA^(2)omega^(2)cos(2omegat+2theta)`
On the right hand side, the first term is a constant - it ensures that the kinetic energy K is never negative. The cosine factor in the second term actually signifies that K is an oscillating quantity. The frequency of the oscillation is
`n.=(2omega)/(2pi)=2*omega/(2pi)=2n`.