Damped oscillations are oscillations with drag force acting on the system, causing the amplitude to decrease exponentially over time. The oscillation frequency depends on the natural frequency, mass, and drag constant. In an underdamped oscillator, the natural frequency is greater than half the drag constant divided by the mass, resulting in a positive oscillation frequency and decreasing amplitude oscillations. Critically damped oscillators have a natural frequency equal to half the drag constant divided by the mass, reaching equilibrium without oscillations. Overdamped oscillators have a natural frequency less than half the drag constant divided by the mass, with no oscillations and a long time to reach equilibrium.