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

Question

Dr. Abubacker · Accepted Answer

(b) Given,
$y = 4\cos^{2}{\frac{t}{2}\sin(1000t)}$
$= 2\left( 1 + \cos t ight)\sin(1000t)\ \left( \because 1 + \cos{	heta = 2\cos^{2}\frac{	heta}{2}} ight)$
$= 2\sin{1000t + 2\cos{t\sin{1000t}}}$
$= 2\sin{1000t + \sin{(1001)t + \sin{(999)t}}}$
Therefore, it consists of 3 SHM’s

Q. The displacement y of a particle is given by$y = 4\cos^{- 4}{\left( \frac{t}{2} \right)\sin(1000t)}$. This expression may be considered to be a result of the superposition of how many simple harmonic motions?

Explanation

Reviewed by Dr. Abubacker

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