Simple Harmonic Motion Calculator NZ

This calculator works out the motion of an object undergoing simple harmonic motion, finding its position, velocity and acceleration at any instant, along with the period of oscillation. Simple harmonic motion, or SHM, is the smooth back-and-forth oscillation that appears throughout physics whenever a restoring force pulls an object back toward a central position in proportion to how far it has strayed. A mass bouncing on a spring, a pendulum swinging through small angles, a vibrating guitar string, and the oscillation of atoms and circuits all follow it. The motion is described by a few key quantities: the amplitude, the maximum displacement from the centre; the frequency, how many oscillations occur per second; and from these the angular frequency and the period. At any moment the object's position traces a cosine curve, its velocity is greatest at the centre and zero at the extremes, and its acceleration is greatest at the extremes and zero at the centre, always pointing back toward the middle. This tool computes them. You enter the amplitude, the frequency, and a time of interest, and the calculator returns the position at that time, the velocity at that time, the maximum velocity, and the period. The results update as you type, so you can trace how the motion evolves. Use it for physics problems on springs, pendulums and waves, for understanding oscillations, or for engineering vibration work. The relationships are clean: the angular frequency is two pi times the frequency, the maximum velocity is the amplitude times the angular frequency, and the maximum acceleration is the amplitude times the angular frequency squared. A defining feature of simple harmonic motion is that the period depends only on the system's properties, not on the amplitude, which is why a pendulum keeps good time whether it swings a little or a lot.

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x = A cos(2 pi f t), with velocity and acceleration following. Max velocity = A x angular frequency. The period depends only on frequency, not amplitude. Rounded for display.