Question

which of the following fractions of time represent (a) periodic and (b) non-periodic motion? give the period for each case of periodic motion?

(i) sin wt + cos wt
(ii) log (wt)
(iii) sin wt + cos2wt + sin 4wt​

Answer 1

Explanation:

a ) (i) sin wt + cos wt

Period = 2 pi / omega

(iii) sin wt + cos2wt + sin4wt

Period = 2 pi / omega

b ) (ii) log ( wt )

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Answer 2

2 is aperiodic

Explanation:

I'll give the shortcut

When 2 periodic functions are added , the one with the greatest period is the answer

1) Both have period 2pi/w so answer is 2pi/w

3) Sin wt has period 2pi/w

Cos 2wt has half the period of coswt as there is a 2 so period pi/w

sin4wt has period pi/2w

So overall period is 2pi/w

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