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
  1. $\sqrt{\frac{k}{m}+\left(\frac{b}{2 m}\right)^2}$
  2. $\frac{\mathrm{k}}{\mathrm{m}}+\left(\frac{\mathrm{b}}{2 \mathrm{~m}}\right)^2$
  3. $\sqrt{\frac{k}{m}-\left(\frac{b}{2 m}\right)^2}$
  4. $\frac{\mathrm{k}}{\mathrm{m}}-\left(\frac{\mathrm{b}}{2 \mathrm{~m}}\right)^2$

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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