Forced Harmonic Resonance of SDOF System

Mechanical Engineering

How It Works

A single-degree-of-freedom spring-mass-damper system subjected to sinusoidal external harmonic excitation exhibits resonant behavior. When the forcing frequency (ω) matches the system's undamped natural frequency (ω_n = √(k/m)), the dynamic magnification factor (DMF) peaks sharply. Viscous damping limits the maximum resonant vibration amplitude and introduces a 90-degree phase lag.

Governing Equation
DMF = 1 / √((1 - (ω/ω_n)²)² + (2 · ζ · ω/ω_n)²) , ω_n = √(k / m) , tan φ = (2ζ · r) / (1 - r²)