The motion of a particle is described by the equation $a=-b x$ where ' $a$ ' is the acceleration, x is the…

The motion of a particle is described by the equation $a=-b x$ where ' $a$ ' is the acceleration, x is the displacement from the equilibrium position and b is a constant. The periodic time will be
  1. $\frac{2 \pi}{\mathrm{~b}}$
  2. $\frac{2 \pi}{\sqrt{\mathrm{~b}}}$
  3. $2 \pi \sqrt{b}$
  4. $2 \sqrt{\frac{\pi}{\mathrm{~b}}}$

Solution

$\begin{aligned} & \text {Given, } a=-b x \\ & \text {But }, a=-\omega^2 x \\ & \therefore \quad \omega=\sqrt{b} \quad ...(i)\\ & \quad T=\frac{2 \pi}{\omega} \\ &=\frac{2 \pi}{\sqrt{b}} \end{aligned}$ .

Asked in: MHT CET 2024 (15 May Shift 2)

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