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(B) Given the equation of motion for the particle is $a = -bx$. Comparing this with the standard equation for Simple Harmonic Motion $(SHM)$,which is

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$\frac{2 \pi}{\sqrt{b}}$

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(B) Given the equation of motion for the particle is $a = -bx$. Comparing this with the standard equation for Simple Harmonic Motion $(SHM)$,which is $a = -\omega^2 x$,where $\omega$ is the angular frequency. Equating the two expressions,we get $\omega^2 = b$,which implies $\omega = \sqrt{b}$. The time period $T$ of an $SHM$ is given by the formula $T = \frac{2 \pi}{\omega}$. Substituting the value of $\omega$,we get $T = \frac{2 \pi}{\sqrt{b}}$.

The motion of a particle is described by the equation $a = -bx$,where $a$ is the acceleration,$x$ is the displacement from the equilibrium position,and $b$ is a constant. The periodic time will be

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