Natural Frequency

Every physical object has a characteristic natural frequency at which it prefers to oscillate when disturbed. For simple mass‑spring systems the frequency follows f = (1/2π)√(k/m), while for tuning forks, wine glasses and cantilever rods the geometry and material properties set the pitch, often scaling with length or shape.

In this simulation students can pull down a mass on a spring, strike a tuning‑fork prong, tap a glass, or hit a steel rod using on‑screen buttons or by dragging the objects. Each object then vibrates at its own frequency, producing a pure tone (or silent motion for very low frequencies) that decays over time, allowing direct comparison of periods, pitches and damping effects.

By observing the motion and listening to the sounds, learners connect mathematical formulas to real‑world phenomena, see how mass, stiffness, length and material affect vibration, and explore concepts such as resonance, overtones and damping in a hands‑on visual and auditory environment.