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(B) The standard differential equation for simple harmonic motion $(SHM)$ is given by $\frac{d^2 x}{d t^2} + \omega^2 x = 0$,which can be rewritten as

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$2 \pi \sqrt{\frac{\alpha}{\beta}}$

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(B) The standard differential equation for simple harmonic motion $(SHM)$ is given by $\frac{d^2 x}{d t^2} + \omega^2 x = 0$,which can be rewritten as $\frac{d^2 x}{d t^2} = -\omega^2 x$.Given equation: $\alpha \frac{d^2 x}{d t^2} + \beta x = 0$.Rearranging the given equation: $\frac{d^2 x}{d t^2} = -\frac{\beta}{\alpha} x$.Comparing this with the standard form $\frac{d^2 x}{d t^2} = -\omega^2 x$,we get $\omega^2 = \frac{\beta}{\alpha}$,which implies $\omega = \sqrt{\frac{\beta}{\alpha}}$.The time period $T$ is given by $T = \frac{2 \pi}{\omega}$.Substituting the value of $\omega$: $T = \frac{2 \pi}{\sqrt{\frac{\beta}{\alpha}}} = 2 \pi \sqrt{\frac{\alpha}{\beta}}$.

$A$ simple harmonic motion is represented by $\alpha \frac{d^2 x}{d t^2}+\beta x=0$. Its period is

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