Damped Oscillation Amplitude Decay Formula — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Damped Oscillation Amplitude Decay Formula Applicable to underdamped harmonic oscillators where the damping force is linearly proportional to velocity (viscous damping). Establish Newton's Second Law with a restoring force and damping force: ma = -kx - bv. Formulate the second-order linear differential equation: mx'' + bx' + kx = 0. Assume a solution of form x(t) = C e pt . Solve the characteristic equation mp 2 + bp + k = 0 to find roots. Isolate the real part of the complex roots (-b/2m) which governs the exponential decay envelope. b 2 < 4mk (Underdamped condition for oscillation to occur) m > 0 t >= 0 Confusing amplitude decay (time constant 2m/b) with energy decay (time constant m/b). Thinking the damping constant b is dimensionless. Applying this exponential decay model to constant friction (Coulomb damping), which decays linearly.