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An oscillation is superposition of three...

An oscillation is superposition of three harmonic oscillations and decribed by the equation `x=A sin 2pi upsilon_(1)` where A changes with time according to `A=A_(0)(1+cos 2pi upsilon_(2)t)` with `A_0` to be constant. The frequencies of pure harmonic oscillations forming this oscillation are

A

`upsilon_(1),upsilon_(2),|upsilon_(1)-upsilon_(2)|`

B

`upsilon_(1),|upsilon_(1)-upsilon_(2)|,upsilon_(1)+upsilon_(2)`

C

`upsilon_(1),upsilon_(2),|upsilon_(2)-upsilon_(1)|`

D

`upsilon_(1),upsilon_(2),upsilon_(1)+upsilon_(2)`

Text Solution

Verified by Experts

`x=A_(0)(1+cos 2pi upsilon_(2)t).sin 2 pi upsilon_(1) t`
`=A_(0) sin 2 pi upsilon_(1) t+(A_(0))/2 [(sin 2pi(upsilon_(1)+upsilon_(2))t+sin 2pi(upsilon_(1)-upsilon_(2))t]`
Hence frequency are
`upsilon_(1)|upsilon_(1)-upsilon_(2)|.upsilon_(1)+upsilon_(2)`
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