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  4. In S.H.M. if the magnitude of maximum acceleration is a and maximum velocity is β, then its time period will be

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Q. In S.H.M. if the magnitude of maximum acceleration is a and maximum velocity is $\beta$, then its time period will be

COMEDKCOMEDK 2011Oscillations

Solution:

Maximum acceleration, $\alpha = \omega^2 A$
Maximum velocity, $\beta = \omega A$
$\therefore \:\:\frac{\alpha}{\beta} =\frac{\omega^2 A}{\omega A} =\omega = \frac{2\pi}{T} $
or ,$T = \frac{2\pi\beta}{\alpha}$