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MHT CET · Physics · Oscillations

A particle is performing simple harmonic motion and if the oscillations are damped oscillations then the angular frequency is given by

  1. A \(\sqrt{\frac{k}{m}+\left(\frac{b}{2 m}\right)^2}\)
  2. B \(\frac{\mathrm{k}}{\mathrm{m}}+\left(\frac{\mathrm{b}}{2 \mathrm{~m}}\right)^2\)
  3. C \(\sqrt{\frac{k}{m}-\left(\frac{b}{2 m}\right)^2}\)
  4. D \(\frac{\mathrm{k}}{\mathrm{m}}-\left(\frac{\mathrm{b}}{2 \mathrm{~m}}\right)^2\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\sqrt{\frac{k}{m}-\left(\frac{b}{2 m}\right)^2}\)

Step-by-step Solution

Detailed explanation

\(\omega^2=\frac{k}{m}, r=\frac{b}{2 m}\)
Angular frequency,
\(\begin{aligned}
\omega^{\prime} & =\sqrt{\left(\omega^2-r^2\right)} \\
& =\sqrt{\frac{k}{m}-\left(\frac{b}{2 m}\right)^2}
\end{aligned}\)