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A particle is executing a simple harmonic motion. Its maximum acceleration is $α$ and maximum velocity is $β .$ Then, its time period of vibration will be

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$\frac{β^{2}}{α}$

$\frac{2 π β}{α}$

$\frac{β^{2}}{α^{2}}$

$\frac{α}{β}$

answer is B.

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Detailed Solution

$\begin{array}{l} α = ω^{2} A ...... (1) \\ β = ω A ........ (2) \end{array}$
$\begin{array}{l} \frac{α}{β} = \frac{ω^{2} A}{ω A} = ω \\ T = \frac{2 π}{ω} = \frac{2 π β}{α} \end{array}$

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