The above four animations illustrate, from top to bottom, the amplitude of:

1. an undamped oscillation of natural frequency $\omega_0=8\pi/5\,\mathrm{rad}\cdot\mathrm{s}^{-1}$.
2. an underdamped oscillation with the same natural frequency as the first and with a damping constant of $\gamma=\omega_0/3$.
3. a critically-damped oscillation with natural frequency $\omega_0$ (and, of course, $\gamma=2\omega_0$).
4. an overdamped oscillation with natural frequency $\omega_0$ and damping constant $\gamma=4\omega_0$.

Below are explicit examples of these four oscillations using pendula of length 38.8 cm (not to scale, obviously):