Q: A mass of 2 kg oscillates on a spring with force constant 50 N/m. By what factor does the frequency of oscillation decrease when a damping force with constant b = 12 is introduced ?

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Sol: $\large \omega_0 = \sqrt{\frac{k}{m}} $

$\large \omega_0 = \sqrt{\frac{50}{2}} = 5 $

$\large \omega = \sqrt{\omega_0^2 – (\frac{b}{2m})^2}$

$\large \omega = \sqrt{5^2 – (\frac{12}{2 \times 2})^2}$

$\large \omega = \sqrt{5^2 – 3^2} = 4 $

So , frequency reduces by 1 Hz or 20 %.