Simple Harmonic Motion Calculator (Mass–Spring)

Angular frequency, period, position, velocity and energy of a mass on a spring.

Results

Angular frequency ω—
Frequency—
Period—
Position x(t)—
Velocity v(t)—
Acceleration a(t)—
Maximum speed—
Total energy—

How to use the Simple Harmonic Motion Calculator

  1. Enter or select: Mass m, Spring constant k, Amplitude A, Time t, Phase φ.
  2. The results (Angular frequency ω, Frequency, Period, Position x(t), Velocity v(t), Acceleration a(t), Maximum speed, Total energy) are calculated instantly as you type.
  3. Use “Copy link” to share the calculation with the same input values.

Formula

  • x(t) = A cos(ωt + φ)
  • ω = √(k/m)
  • E = ½kA²
ExpressionApply operationsCalculated result