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# how to decide a fuction is a periodic,or non periodicand simple hormonic.sin square omega t" is it a periodic or simple hormonic?pl explain

Asked by mvenkataram 1st December 2018, 3:50 AM
If a time dependent function repeats its value at any given time, after a muliple times of time period, then this function is periodic.

Example:- Let f(t) = sin ωt , where ω = 2π/T

The function value at t' will be repeated  after t'+nT , where n = 0,1,2,3.....etc . Hence the above function f(t) is periodic with time period T

if there is no repetation of value of the function at any given time, then it is non-periodic.

If the second derivative of function with respect to time is proportional to the function itself, then the function is simple harmonic.

f(t) = sin2ωt

since sin(ωt)  is periodic as given in the example, sin2(ωt) also periodic.
But it can be seen that second derivative of sin2(ωt) is not proportional to sin2(ωt), it is not simple harmonic
Answered by Expert 3rd December 2018, 4:05 AM
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