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
AIPMT 2015, Medium
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If $A$ and $\omega$ be amplitude and angular frequency of vibration, then
${\alpha=\omega^{2} A} ......... (i)$
${\text { and } \beta=\omega A} ......... (ii)$
Dividing eqn. $(i)$ by eqn. $(ii),$ we get
$\frac{\alpha}{\beta}=\frac{\omega^{2} A}{\omega A}=\omega$
$\therefore$ Time period of vibration is
$T=\frac{2 \pi}{\omega}=\frac{2 \pi}{(\alpha / \beta)}=\frac{2 \pi \beta}{\alpha}$
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