Which of the following functions of time represent (a) simple har… - Vidyadip

Question

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):$\sin^3\omega\text{t}$

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Answer

Periodic, but not SHM The given function is:$\sin^3\omega\text{t}$
$=\frac{1}{2}[3\sin\omega\text{t}-\sin3\omega\text{t}]$
The terms $\sin\omega\text{t}$ and $\sin\omega\text{t}$ individually represent simple harmonic motion (SHM).
However, the superposition of two SHM is periodic and not simple harmonic.

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