First slide

Simple harmonic motion

Question

A particle is executing simple harmonic motion with frequency f. The frequency at which its kinetic energy change into potential energy is

Easy

A

f/2
B

f
C

2 f
D

4 f

Solution

$K E = \frac{1}{2} m v^{2} = \frac{1}{2} m {(ω A \cos ω t)}^{2} = \frac{1}{2} m ω^{2} A^{2} \cos^{2} ω t = \frac{1}{2} m ω^{2} A^{2} \frac{[1 + \cos 2 ω t]}{2} = \frac{1}{4} m ω^{2} A^{2} + \frac{1}{4} m ω^{2} A^{2} \cos 2 ω t$
In S.H.M., frequency of K.E. and P.E.
= 2 $\times$ (Frequency of oscillating particle)

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