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x=ASin(\omega t) +BSin(2\omega t) represents 

Option: 1

Periodic function


Option: 2

SHM equation


Option: 3

Both A and B


Option: 4

None of these


Answers (1)

best_answer

For 

x=ASin(\omega t) +BSin(2\omega t)

x(t)=ASin(\omega t) +BSin(2\omega t) ........ (1)

x(t+T)=ASin(\omega (t+T)) +BSin(2\omega (t+T))\\ \Rightarrow x(t+T)= ASin(\omega t+\omega T) +BSin(2\omega t+2\omega T) \\ \\ \Rightarrow x(t+T)= ASin(\omega t+2\pi) +BSin(2\omega t+4\pi) \\ \Rightarrow x(t+T)=ASin(\omega t) +BSin(2\omega t) ....... (2)

From equation (1) and (2)

we get

x (t)=x(t+T)

So it is a periodic function

and

as the condition of SHM i.e acceleration=a=\frac{d^2(x) }{d t^2} \ \alpha \ -x

is not followed by the equation x=ASin(\omega t) +BSin(2\omega t)

So this is not the SHM equation.

Posted by

Suraj Bhandari

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