A particle is performing simple harmonic motion and if the oscillations are damped oscillations then the…
A particle is performing simple harmonic motion and if the oscillations are damped oscillations then the angular frequency is given by
- $\sqrt{\frac{k}{m}+\left(\frac{b}{2 m}\right)^2}$
- $\frac{\mathrm{k}}{\mathrm{m}}+\left(\frac{\mathrm{b}}{2 \mathrm{~m}}\right)^2$
- $\sqrt{\frac{k}{m}-\left(\frac{b}{2 m}\right)^2}$
- $\frac{\mathrm{k}}{\mathrm{m}}-\left(\frac{\mathrm{b}}{2 \mathrm{~m}}\right)^2$
Solution
$\omega^2=\frac{k}{m}, r=\frac{b}{2 m}$
Angular frequency,
$\begin{aligned}
\omega^{\prime} & =\sqrt{\left(\omega^2-r^2\right)} \\
& =\sqrt{\frac{k}{m}-\left(\frac{b}{2 m}\right)^2}
\end{aligned}$
Asked in: MHT CET 2024 (02 May Shift 1)
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