Question

Find the frequency of osculation of an underdamped harmonic oscillator of mass $m$ in terms of its natural frequency ${\omega }_0$ and damping constant $\gamma$ (where - $vy$ is the damping force, $v$ being the velocity)

Answer 1

$ma=-nx-cv$ for damped oscillator equation for under damped oscillator

$x=e^{-rt}\cos (w,t-\varphi )$

Where $r=\frac{c}{2m}$ (damping constant)

$w_0=\sqrt{\frac{n}{m}}$ (frequency of natural oscillation )

$w_1=\sqrt{w_0^2-\frac{C^2}{4m^2}}$

$\Rightarrow w_1=\sqrt{w_0^2-r^2}$