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Home » 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 (w is any positive constant):(a) (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 (w is any positive constant):
(a) 3 \cos (\pi / 4-2 \omega t)
(b) \cos \omega t+\cos 3 \omega t+\cos 5 \omega t
CBSE | Class 11 | NCERT | Oscillations | Physics
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 (w is any positive constant):
(a) 3 \cos (\pi / 4-2 \omega t)
(b) \cos \omega t+\cos 3 \omega t+\cos 5 \omega t

(a) 3 \cos [4 \pi-2 \omega t]=3 \cos [2 \omega t-\pi / 4]

The equation can be written in the form \cos (\omega t+\phi). It is S.H.M with the period 2 \pi / 2 \omega=\pi / \omega

(b) \cos \omega t+\cos 3 \omega t+\cos 5 \omega t.

A basic harmonic motion is represented by each cosine function. The superposition of three simple harmonic motions, on the other hand, is periodic, but it is not simple harmonic. It has a 2 \pi / \omega time span.

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