If the maximum acceleration of a S.H.M. is $α$ and the maximum velocity is ß then amplitude of vibration is given by

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$β^{2} α$

$\frac{α^{2}}{β}$

$\frac{β^{2}}{α}$

$α^{2} β$

answer is C.

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Detailed Solution

$\begin{array}{l} a_{max} = α = ω^{2} A A = ? \\ v_{max} = β = ωA \\ ωA = β \Rightarrow \frac{ω^{2} A}{ωA} = \frac{α}{β} ω = α / β \frac{α}{β} A = β \Rightarrow A = \frac{β^{2}}{α} \end{array}$

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