AI authored to showcase ironpad capabilities.
The spring-mass-damper (SMD) is a fundamental mechanical model used in vibration analysis, control theory, and engineering design. A mass m slides on a frictionless surface, coupled to a fixed wall by a spring with stiffness k and a viscous damper with coefficient c.
Newton's second law yields the linear ODE:
m\ddot{x} + c\dot{x} + kx = F(t)
where x is displacement from equilibrium, \dot{x} velocity, \ddot{x} acceleration, and F(t) an optional external force.
| Regime | Condition | Response |
|---|---|---|
| Underdamped | \zeta < 1 | Decaying oscillation, bounces before settling |
| Critically damped | \zeta = 1 | Fastest return with no overshoot |
| Overdamped | \zeta > 1 | Sluggish exponential decay, no oscillation |
Enable External Forcing to apply F(t) = A\sin(\omega_f t). When the driving frequency \omega_f approaches \omega_n, resonance amplifies the response, especially for low damping.
Adjust the sliders to move between regimes and watch the physical diagram, waveform, and dashboard update live.
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