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Question -

Which of the following functionof time represent (a) simple harmonic, (b) periodic but not simple harmonic,and (c) non-periodic motion? Give period for each case of periodic motion (tois any positive constant).
(a) sin wt – cos wt (b) sin2 wt(c) 3 cos -2 cos (π/4-2 wt) (d) cos wt + cos 3 wt + cos 5 wt
(e) exp (- w2t2) (f) 1 + wt + w2t2.



Answer -

Thefunction will represent a periodic motion, if it is identically repeated aftera fixed interval of time and will represent S.H.M if it can be written uniquelyin the form of a cos

(e) e-w2t2 . It is an exponential function which never repeats itself. Therefore it represents non-periodic motion.
(f) 1 + wt + w2t2 also represents non periodic motion.

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