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how to decide a fuction is a periodic,

or non periodic

and simple hormonic.

sin square omega t" is it a periodic or simple hormonic?

pl explain

Asked by mvenkataram 1st December 2018, 3:50 AM
Answered by Expert
Answer:
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
 
begin mathsize 12px style fraction numerator d f over denominator d t end fraction equals space 2 omega space sin omega t space cos omega t
fraction numerator d squared f over denominator d t squared end fraction equals space 2 omega squared open square brackets negative sin squared omega t space plus cos squared omega t close square brackets equals space 2 omega squared space cos space 2 omega t end style
 
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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