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
- A \(\sqrt{\frac{k}{m}+\left(\frac{b}{2 m}\right)^2}\)
- B \(\frac{\mathrm{k}}{\mathrm{m}}+\left(\frac{\mathrm{b}}{2 \mathrm{~m}}\right)^2\)
- C \(\sqrt{\frac{k}{m}-\left(\frac{b}{2 m}\right)^2}\)
- D \(\frac{\mathrm{k}}{\mathrm{m}}-\left(\frac{\mathrm{b}}{2 \mathrm{~m}}\right)^2\)
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,
\(\begin{aligned}
\omega^{\prime} & =\sqrt{\left(\omega^2-r^2\right)} \\
& =\sqrt{\frac{k}{m}-\left(\frac{b}{2 m}\right)^2}
\end{aligned}\)
Angular frequency,
\(\begin{aligned}
\omega^{\prime} & =\sqrt{\left(\omega^2-r^2\right)} \\
& =\sqrt{\frac{k}{m}-\left(\frac{b}{2 m}\right)^2}
\end{aligned}\)
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