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Real oscillating systems lose energy to friction. With linear damping force $F_d = -bv$, the equation of motion is $m\ddot{x} + b\dot{x} + kx = 0$. The solution depends on the damping parameter $\gamma = b/(2m)$ relative to the natural frequency $\omega_0 = \sqrt{k/m}$.

Underdamped ($\gamma < \omega_0$): $x = A_0 e^{-\gamma t}\sin(\omega' t + \phi)$ where $\omega' = \sqrt{\omega_0^2-\gamma^2}$ (frequency decreases slightly). Amplitude decays exponentially. Critically damped ($\gamma = \omega_0$): fastest return to equilibrium without oscillation. Used in car shock absorbers and galvanometers. Overdamped ($\gamma > \omega_0$): slow exponential return, no oscillation. Energy decays as $E(t) = E_0 e^{-2\gamma t} = E_0 e^{-bt/m}$, at twice the rate of amplitude decay since $E \propto A^2$. The quality factor $Q = \omega_0/(2\gamma) = \pi f_0 m/b$ measures how many oscillations occur before significant energy loss. High $Q$ means low damping and sharp resonance. Time for energy to fall to $1/e$:$\tau = m/b$.$