Simple Harmonic Motion Calculator (or Sinusodial (Sine) Motion Calculator) to calculate frequency, displacement, velocity and acceleration values of sinusoidal motion.

Consider the harmonic motion of a periodic waveform shown in the figure. The waveform will repeat itself every 360° or expressed mathematically every 2π radians. If we look at the displacement curve in figure, we can define an instantaneous displacement at a time using displacement formula for sinusoidal motion.

Sinusoidal motion / Simple Harmonic Motion (displacement - velocity - acceleration)

The differential of displacement formula will give us the instantaneous velocity v. If we now differentiate the velocity formula, we can solve for instantaneous acceleration a.

By using these formulas and selecting phase angles accordingly, maximal values of displacement, velocity and acceleration of a simple harmonic motion can be obtained.

Equipments and structures which will work in a vibratory environment are generally qualified to this environment in vibration test labs. There are different kinds of environmental vibration tests such as random, shock and sine sweep vibration tests. These environmental vibration tests are generally done with electrodynamic shakers. This calculator can be used to calculate sinusoidal vibration parameters for sine vibration test and check whether a vibration shaker test system can perform a sine vibration test within the shaker's specifications.

Simple Harmonic Motion Calculator:

Unit system selection
(Hz, mm, mm/s, g)

(Hz, in, in/s, g)
Known parameters
Frequency Hz
Displacement (peak-to-peak) mm


Note: Use dot "." as decimal separator.

Parameter Value

Note: Default rounding is 5 decimal places.

Simple Harmonic Motion Equations:

Displacement formula x=Dsin(2πft)/2
Velocity formula v=πfDcos(2πft)
Acceleration formula a=-2π2f2Dsin(2πft)
Displacement peak to peak value D
The time in seconds t
The frequency in Hertz f