SDOF Vibration Simulator

Explore the dynamics of a Single-Degree-of-Freedom system. Adjust parameters to see real-time response.

u(t) F(t)

Theory & Guide

System Parameters

  • m (Mass): Inertia of the system (kg).
  • k (Stiffness): Resistance to deformation (N/m).
  • c (Damping): Energy dissipation coefficient (N·s/m).

Forcing

  • F₀ (Amplitude): Magnitude of external force (N).
  • p (Frequency): Frequency of external force (rad/s).

Fundamental Equations

Natural Frequency: ωₙ = √(k/m)

Damping Ratio: ζ = c / (2√(km))

Damping Regimes

  • Underdamped (ζ < 1): Oscillates with decaying amplitude.
  • Critically Damped (ζ = 1): Fastest return to equilibrium without oscillation.
  • Overdamped (ζ > 1): Slow return to equilibrium without oscillation.
Simulation Tip: For Free Vibration, set F₀ = 0 and adjust Initial Displacement (u₀) or Velocity (v₀).
1.0
100
5.0
10
5.0
0.0
0.0
Natural Frequency (ωn) --
Damping Ratio (ζ) --
Regime --
Peak Disp. --
Peak Vel. --

System Equation

Displacement u(t)

Velocity u'(t)