SubjectCalc

mechanics

Simple Harmonic Motion Calculator

Calculate spring-oscillator or small-angle pendulum period, frequency, angular frequency, phase, instantaneous displacement, velocity, acceleration, energy, and a motion curve.

Calculator

Ideal mass-spring oscillator.

Formula

ωspring=√(k/m); ωpendulum=√(g/L); T=2π/ω; f=1/T; x=Acos(ωt+φ); v=−Aωsin(ωt+φ); a=−ω²x; E=½kA²

Assumptions and limits

  • The spring is ideal; pendulum mode uses the small-angle approximation up to about 20°.

Example

Spring oscillator

The calculator starts with an editable example.

Sources

Frequently asked questions

Are my inputs uploaded?

No. This calculator runs locally in your browser. Inputs are placed in a URL only when you explicitly copy a share link.

Why are units converted first?

Canonical units prevent scale errors when inputs use mixed units. The result is converted back to your selected output unit afterward.

Does the result replace professional judgment?

No. The result applies only to the stated model and assumptions. Qualified people should review high-risk engineering, medical, or laboratory decisions.