The displacement $y$ of a particle executing periodic motion is given by $y = 4\cos^{2}{(t/2)\sin{(1000t)}}.$ This expression may be considered to be a result of the superposition of…….. independent harmonic motions

Question

Dr. Abubacker · Accepted Answer

(b) $y = 4\cos^{2}{\left( \frac{t}{2} \right)\sin{1000\ t}}$
$\Rightarrow y = 2\left( 1 + \cos t \right)\sin{1000\ t}$
$\Rightarrow y = 2\sin{1000\ t} + 2\cos{t\sin{1000\ t}}$
$\Rightarrow y = 2\sin{1000\ t} + \sin 999t + \sin{1001\ t}$
It is a sum of three S.H.M.

Q. The displacement $y$ of a particle executing periodic motion is given by $y = 4\cos^{2}{(t/2)\sin{(1000t)}}.$ This expression may be considered to be a result of the superposition of…….. independent harmonic motions

Explanation

Reviewed by Dr. Abubacker

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