Damped Harmonic Oscillator Dynamics

Mechanical Engineering

How It Works

A damped harmonic oscillator consists of a mass attached to a linear spring and viscous dashpot damper. When displaced from equilibrium, the system experiences a Hookean restoring force proportional to displacement and a viscous drag force proportional to velocity. Underdamped systems oscillate with an exponentially decaying amplitude envelope governed by the damping ratio (ζ) and natural frequency (ω_n).

Governing Equation
m · d²x/dt² + c · dx/dt + k · x = 0 , x(t) = X₀ · e^(-ζ · ω_n · t) · cos(ω_d · t - φ)