This simulator drives a damped mass-spring oscillator with a sinusoidal force at a frequency you choose, while you separately set the system's own natural frequency and its damping level. A live animated mass bounces at the resulting steady-state amplitude, while a response curve on the right plots amplitude ratio against driving frequency and marks exactly where you are on that curve.
• A live animated mass-spring system oscillating at the steady-state amplitude produced by your chosen driving frequency, natural frequency and damping. • A response curve plotting amplitude ratio versus driving frequency for the current damping level, with a dashed marker at the natural frequency and a moving dot at your current operating point. • Live readouts for the steady-state amplitude ratio and how far the driving frequency is detuned from the natural frequency. • Independent sliders for driving frequency, natural frequency, and damping so you can explore the classic resonance peak from every angle.
A driven damped oscillator settles into steady-state motion at the driving frequency, with an amplitude set by how close that driving frequency sits to the system's natural frequency and how much damping resists the motion. With little damping, the amplitude at resonance can grow dramatically — this is the same effect that lets a marching cadence collapse a bridge or lets a singer shatter a glass by matching its natural frequency. Increasing damping broadens and flattens the resonance peak, trading peak amplitude for a gentler, more forgiving response across a wider range of driving frequencies.
Resonance occurs when a system is driven at a frequency close to its own natural frequency, causing the amplitude of oscillation to build up, often dramatically, compared to driving it far from that frequency.
Damping is what limits how much energy can accumulate in the oscillator at resonance. With very little damping, energy keeps building each cycle since little is dissipated, allowing amplitude to grow to many times what a low-frequency, non-resonant drive would produce.
For a damped oscillator, the peak of the amplitude response curve occurs very close to, but technically slightly below, the undamped natural frequency, with the shift becoming more noticeable as damping increases — you can see the response-curve marker sit just left of the dashed natural-frequency line for higher damping.
It models a single-degree-of-freedom linear damped oscillator under ideal steady-state sinusoidal forcing — there is no transient startup behavior, nonlinear stiffness, or multi-mode coupling of the kind found in complex real structures.