Question

A particle is executing simple harmonic motion with frequency f. Find the frequency of oscillation of kinetic energy.

Solution

Kinetic energy of particle executing simple harmonic motion is given by,

straight K equals 1 half mv squared space space equals 1 half mω squared straight A squared cos squared 2 πft space space equals straight E space cos squared ωt equals straight E open parentheses fraction numerator 1 plus cos 4 πft over denominator 2 end fraction close parentheses space space equals straight E over 2 plus fraction numerator Ecos space 2 straight pi left parenthesis 2 straight f right parenthesis straight t over denominator 2 end fraction

The first term is constant and second term is oscillatory having frequency 2f.
Thus the frequency of oscillation of kinetic energy is 2f.

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