If a damped oscillator is very heavily damped,what is its frequency?

$A$ simple harmonic oscillator of angular frequency $\omega = 2 \, rad \, s^{-1}$ is acted upon by an external force $F = \sin(t) \, N$. If the oscillator is at rest in its equilibrium position at $t = 0$,its position at later times is proportional to

The amplitude of vibration of a particle is given by $a_m = \frac{a_0}{a\omega^2 - b\omega + c}$,where $a_0, a, b,$ and $c$ are positive constants. The condition for a single resonant frequency is:

Explain the behaviour of the oscillator when the driving frequency is far from the natural frequency in small damped oscillations.

The value of maximum possible amplitude in the case of forced oscillations when the driving frequency is close to the natural frequency is:

The amplitude of a mass-spring system,which is executing simple harmonic motion,decreases with time. If mass $m = 500 \, g$,and the decay constant $b = 20 \, g/s$,then how much time $t$ (in seconds) is required for the amplitude of the system to drop to half of its initial value? (Given $\ln 2 = 0.693$)