engineering

Simple Harmonic Motion Calculator

Calculate period, frequency, and max velocity for spring-mass systems

Simple Harmonic Motion Calculator

Calculate SHM properties for a spring-mass system.

Angular Freq. ω

10.0000 rad/s

Period T

0.6283 s

Frequency f

1.5915 Hz

Max Velocity v_max

1.0000 m/s

Max Acceleration a_max

10.0000 m/s²

Total Energy E

0.5000 J

Formulas

ω = √(k/m) = √(100.0/1.0) = 10.0000 rad/s
T = 2π/ω = 0.6283 s
f = 1/T = 1.5915 Hz
v_max = Aω = 1.0000 m/s
a_max = Aω² = 10.0000 m/s²
E = ½kA² = 0.5000 J

How to Use This Calculator

1

Enter your input values

Fill in all required input fields for the Simple Harmonic Motion Calculator. Most fields include unit selectors so you can work in your preferred unit system.

2

Review your inputs

Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors.

3

Read the results

The Simple Harmonic Motion Calculator instantly computes the output and displays results with units. All calculations happen in your browser — no loading time and no data sent to a server.

Formula Reference

Simple Harmonic Motion Calculator Formula

See calculator inputs for the governing equation

Variables: All variables and their units are labeled in the calculator interface above.

When to Use This Calculator

  • •Use the Simple Harmonic Motion Calculator when solving homework or exam problems that require quick numerical verification of your hand calculations.
  • •Use it during the design phase to rapidly iterate on parameters before running detailed finite element simulations.
  • •Use it when reviewing a colleague's calculation or checking a vendor's data sheet for plausibility.
  • •Use it to generate reference data for a technical report or presentation without manual computation.

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