In damped SHM with damping force $F_d = -bv$, the amplitude decays as $A(t) = A_0 e^{-\gamma t}$ where $\gamma = b/(2m)$ is the damping coefficient. The angular frequency changes to $\omega' = \sqrt{\omega_0^2 - \gamma^2}$. Energy decays as $E(t) = E_0 e^{-2\gamma t}$. Three regimes: underdamped ($\gamma < \omega_0$, oscillation with decay), critically damped ($\gamma = \omega_0$, fastest non-oscillatory return), overdamped ($\gamma > \omega_0$, slow exponential return). Quality factor $Q = \omega_0/(2\gamma)$ measures sharpness of resonance.