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  • Which of the following functions of time represent ,(a) simple harmonic

Q. 14.4 (a) 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):

(a)  sin\; \omega t-cos\; \omega t

Answers (1)

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\\sin\omega t-cos\omega t\\ =\sqrt{2}\left ( \frac{1}{\sqrt{2}}sin\omega t-\frac{1}{\sqrt{2}}cos\omega t \right )\\ =\sqrt{2}(cos\frac{\pi }{4}sin\omega t-sin\frac{\pi }{4}cos\omega t)\\ =\sqrt{2}sin(\omega t-\frac{\pi }{4})

Since the above function is of form Asin(\omega t+\phi ) it represents SHM with a time period of \frac{2\pi }{\omega }

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Sayak

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