First slide

Simple hormonic motion

Question

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

Moderate

A

Two
B

Three
C

Four
D

Five

Solution

$y = 4 \cos^{2} (\frac{t}{2}) \sin 1000 t$
$\Rightarrow y = 2 (1 + \cos t) \sin 1000 t$
$\Rightarrow y = 2 s i n 1000 t + 2 c o s t s i n 1000 t$
$\Rightarrow y = 2 \sin 1000 t + \sin 999 t + \sin 1001 t$
It is a sum of three S.H.M.

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