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A particle is executing a simple harmonic motion. Its maximum acceleration is $\alpha$ and maximum velocity is $\beta$. Then, its time period of vibration will be:
A
$\frac{2\pi\beta}{\alpha}$
B
$\frac{\beta^2}{\alpha^2}$
C
$\frac{\alpha}{\beta}$
D
$\frac{\beta^2}{\alpha}$
Detailed Solution
Maximum acceleration $= \omega^2A = \alpha$; maximum velocity $= \omega A = \beta$
$\omega = \frac{\alpha}{\beta}$
$T = \frac{2\pi}{\omega} = \frac{2\pi\beta}{\alpha}$
$\omega = \frac{\alpha}{\beta}$
$T = \frac{2\pi}{\omega} = \frac{2\pi\beta}{\alpha}$