InterviewSolution
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InterviewSolution
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Which of the following functions of time represent (a) S.H.M., and (b) periodic but not simple harmonic motion? Give the period for each case: (i) sin ωt - cos ωt(ii) sin2 ωt. |
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Answer» (i) sin ωt - cos ωt = \(\sqrt 2[sin\,\omega tcos\frac{\pi}{4}-\,cos\,\omega t\,sin\,\frac{\pi}{4}]\) = \(\sqrt 2\, sin\,(\omega t\,-\,\frac{\pi}{4})\) This function represents S.H.M., having period T = \(\frac{2\pi}{\omega}\) and initial phase = − \(\frac{\pi}{4}\)rad. (ii) sin2ωt = (1 – cos2ωt) The function is periodic, having a period T = \(\frac{2\pi}{2\omega}=\frac{\pi}{\omega}\) But does not represent S.H.M. |
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