The acceleration displacement $(a - x)$ graph of a particle executing simple harmonic motion is shown in the figure. Find the frequency of oscillation.

\frac{1}{2 π} \sqrt{\frac{β}{α}}

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\frac{1}{2 π} \sqrt{\frac{α}{β}}

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\frac{1}{2 π} \sqrt{\frac{β}{2 α}}

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\frac{1}{2 π} \sqrt{\frac{2 β}{α}}

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Solution

The correct option is A $\frac{1}{2 π} \sqrt{\frac{β}{α}}$
Equation of given graph will be,
$a = - \frac{β}{α} X$ ....(1)
$a = - ω^{2} X$ ...(2)
Comparing both equations, $ω = \sqrt{\frac{β}{α}}$
So, frequency, $f = \frac{ω}{2 π} = \frac{1}{2 π} \sqrt{\frac{β}{α}}$

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