MHT CET · Physics · Oscillations
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
- A \(\frac{2 \pi}{\mathrm{~b}}\)
- B \(\frac{2 \pi}{\sqrt{\mathrm{~b}}}\)
- C \(2 \pi \sqrt{b}\)
- D \(2 \sqrt{\frac{\pi}{\mathrm{~b}}}\)
Answer & Solution
Correct Answer
(B) \(\frac{2 \pi}{\sqrt{\mathrm{~b}}}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned}
& \text {Given, } a=-b x \\
& \text {But }, a=-\omega^2 x \\
& \therefore \quad \omega=\sqrt{b} \quad ...(i)\\
& \quad T=\frac{2 \pi}{\omega} \\
&=\frac{2 \pi}{\sqrt{b}}
\end{aligned}\)
& \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}\)
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