Free, Forced and Damped Oscillations — Prelims Questions

A mass $m$ is attached to a spring of spring constant $k$. When it oscillates in a medium, it experiences a damping force $F_d = -bv$, where $v$ is its velocity. If the natural angular frequency of the undamped system is $omega_0$, what is the angular frequency of the damped oscillation?

Which of the following statements is TRUE regarding resonance in a forced, damped oscillator?

A simple pendulum of length $L$ oscillates in air. If its initial amplitude is $A_0$, and after $N$ oscillations its amplitude reduces to $A_0/e$, what is the damping factor $gamma$ in terms of $N$, $L$, and $g$?

A forced oscillator is subjected to a driving force $F = F_0 sin(omega t)$. The amplitude of the steady-state oscillation is maximum when the driving frequency $omega$ is equal to:

A system is undergoing forced oscillations. If the damping is increased, what happens to the resonance peak in the amplitude vs. driving frequency graph?

Which of the following systems is an example of critically damped motion?