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What is the time - period of x = A sin ...

What is the time - period of `x = A sin (omega t + alpha)`?

Text Solution

Verified by Experts

It is know from trigonometry that
`sin theta = sin(theta + 2 pi)`
Hence `x= A sin (omega t + alpha + 2 pi) = A sin{ omega (t + (2 pi)/(omega)) + alpha}`
`x = A sin omega t + alpha)`, where `t = t + (2 pi)/(omega)`
This shown that the function at `t` coincider with the function at `t`. The interval `(t' - t)` is the period of `x`
This period is `(2 pi)/(omega)`
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