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  • Which of the following functions of time represent (a) simple harmonic, (b) periodic but not simple harmonic (b) sin^3 ωt

Q. 14.4 (b) Which of the following functions of time represent (a) simple harmonic, (b) periodic but not simple harmonic, and (c) non-periodic motion? Give period for each case of periodic motion (\omega is any positive constant):

(b) sin^{3}\omega t

Answers (1)

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\\sin3\omega t =3sin\omega t -4sin^{3}\omega t \\sin^{3}\omega t=\frac{1}{4}\left ( 3sin\omega t - sin3\omega t \right )\\

The two functions individually represent SHM but their superposition does not give rise to SHM but the motion will definitely be periodic with a period of \frac{2\pi }{\omega }

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Sayak

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