Question #42129

A damped harmonic oscillator of mass $m = 0.2\text{ kg}$ is submerged in a viscous fluid. The damping force is given by $F_d = -b v$, where the damping coefficient $b$ depends on the absolute temperature $T$ (in Kelvin) of the fluid as $b = \alpha T$, with $\alpha = 4 \times 10^{-3}\text{ kg s}^{-1}\text{ K}^{-1}$. The temperature of the fluid is measured using a faulty linear thermometer scale $^\circ X$. On this scale, the freezing point of water is $20^\circ X$ and the boiling point of water is $120^\circ X$ (at standard atmospheric pressure). During the experiment, the faulty thermometer reads $47^\circ X$, and the damped angular frequency of the oscillator is measured to be $\omega_d = 4\text{ rad s}^{-1}$. What is the undamped natural angular frequency $\omega_0$ of the oscillator?