Simple Harmonic Motion Calculator
Work out simple harmonic motion instantly with clear inputs, formula shown and shareable results.
About Simple Harmonic Motion Calculator
In simple harmonic motion displacement is sinusoidal, so velocity peaks at A.omega as the body passes through the centre and acceleration peaks at A.omega^2 at the extremes. A 50 mm amplitude at 2.5 Hz gives 0.785 m/s and 12.3 m/s2. Notice acceleration scales with the square of frequency, which is why vibration becomes destructive as frequency rises.
Formulas
Angular frequency
omega = 2 pi f
Peak values
v(max) = A omega; a(max) = A omega^2
Worked example
With the default values below, Simple Harmonic Motion Calculator returns Maximum Velocity of 0.7854. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Amplitudeminimum 0 m
- 0.05 m
- Frequencyminimum 0 Hz
- 2.5 Hz
Results
- Maximum Velocity
- 0.7854 m/s
- Maximum Acceleration
- 12.3370 m/s2
- Angular Frequency
- 15.7080 rad/s
- Period
- 0.4000 s
Step by step
- 1Values used
- 2Angular frequency
- 3Peak values
- 4Maximum Velocity= 0.7854 m/s
- 5Maximum Acceleration= 12.3370 m/s2
- 6Angular Frequency= 15.7080 rad/s
- 7Period= 0.4000 s
Assumptions and limits
- The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax or fees or charges into account.
- Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
Where is the velocity zero?
At the two extremes of the swing, where the body reverses. That is exactly where acceleration is greatest.
What makes motion harmonic?
A restoring force proportional to displacement. Springs and small-angle pendulums qualify; large-angle pendulums do not.