SINUSOIDAL (SINE) MOTION CALCULATOR (VIBRATION CALCULATOR)
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.
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 can be obtained.
Sinusoidal motion calculator was developed to calculate frequency, displacement,
velocity and acceleration values of sinusoidal motion by using these formulas.
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.
Calculator:
INPUT PARAMETERS 
Unit system selection 
(Hz, mm, mm/s, g) 
(Hz, in, in/s, g) 
Known parameters 

Frequency


Hz

Displacement (peaktopeak)


mm



Note: Use dot "." as decimal separator.
RESULTS 
Parameter 
Value 
Unit 
Frequency


[Hz] 
Displacement (peaktopeak) 

[mm]

Velocity (peak) 

[mm/s]

Acceleration (peak) 

[g] 
Note: Default rounding is 5 decimal places.
List of Equations:
Displacement formula 
x=Dsin(2πft)/2 
Velocity formula 
v=πfDcos(2πft) 
Acceleration formula 
a=2π^{2}f^{2}Dsin(2πft) 
Displacement peak to peak value 
D 
The time in seconds 
t 
The frequency in Hertz 
f 