Damped Oscillations
Oscillatory motion whose mechanical energy and amplitude decrease exponentially over time due to dissipative forces like friction or viscosity.
Governing formula
x(t) = A exp(-b t / 2m) cos(ω_d t + φ)
SI unit
m
In depth
System damping can be underdamped (oscillates with decaying amplitude), critically damped (returns to equilibrium as fast as possible without oscillating), or overdamped (slow return without oscillation).
Examples in the real world
Automobile shock absorbers critically damped to absorb road bumps smoothly without bouncing.