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Sinusoidal Motion Calculator 
To use the above calculator:
There is a mathematical relationship between frequency, displacement, velocity, and acceleration for sinusoidal motion when considering their peak values. The relationship is such that if any two of the four variables are known, the other two can be calculated. The equations below provide all the combinations required.
G in these formulas is not the acceleration of gravity. It is a constant for calculation within different systems. For metric, G is 9.80665 m/s². For Imperial, G is 386.0885827 in/s² For SI, G is 1 m/s² Since the motion is sinusoidal, the displacement, velocity, and acceleration are changing sinusoidally. However, they are not in phase. The phase relationship between displacement, velocity, and acceleration is that such that velocity is 90° out of phase with acceleration and displacement is 180° out of phase with acceleration. In other words, when displacement is at a maximum, velocity is at a minimum, and acceleration is at a maximum. 20 Hz Sinusoidal Motion Another use of this calculator is to determine the maximum frequency responses for SpaceAge Control position transducers. To do this, refer to data sheets located in our (Literature Room) and note the maximum acceleration for a given model. Then, use this calculator to determine the model's maximum frequency for a given displacement and related information. Equations, graphs, and information are courtesy of Richard Baker who produces VIBKIT, a comprehensive vibration testing toolkit that has a demo version available. Note: 1 gn = 9.80665 m/s² = 32.174 ft/s² = 386.0886 in/s². Other calculators:
No Warranties: This calculator and information are provided "as is" without any warranty, condition, or representation of any kind, either express or implied, including but not limited to, any warranty respecting noninfringement, and the implied warranties of conditions of merchantability and fitness for a particular purpose. In no event shall SpaceAge Control, Inc. be liable for any direct, indirect, special, incidental, consequential or other damages howsoever caused whether arising in contract, tort, or otherwise, arising out of or in connection with the use or performance of the information contained on this Web page. 