Question

# A particle executes simple harmonic motion with a frequency $$'f'$$. The frequency with which its kinetic energy oscillates is?

A
f2
B
f
C
2f
D
4f

Solution

## The correct option is C $$2f$$Let, $$x=A\sin\omega t$$$$v=\cfrac {dx}{dt}=A\omega \cos \omega t$$Kinetic energy, $$K=\cfrac {1}{2}mv^2$$$$\implies K=\cfrac {1}{2}m\omega ^2A^2\cos^2\omega t$$$$\implies K=\cfrac {1}{2}m\omega^2A^2\left (\cfrac {1+cos2\omega t}{2}\right)$$$$\implies K=\cfrac {1}{4}m\omega^2A^2(1+\cos^2\omega t)$$$$\therefore \omega_K=2\omega$$$$\therefore$$ Frequency of oscillation of K.E $$=2f\quad \left[f=\cfrac {\omega}{2\pi}\right]$$Physics

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