# Generating Sine Waves, Easy for the RMC, but....

Generating sine waves or sinusoidal motion is more difficult that you think. It is easy to use the sine start command to make the target generator generate sine wave. The real problem is the mechanics and hydraulics. As the frequency increases the peak velocity is proportional to the frequency. This is is expected but what surprises people is that the peak acceleration is proportional to the frequency squared. From experience it is relatively easy to generate sine waves up to 10 Hz depending on the amplitude of the sine wave. Generating sine wave at 100 Hz approaches the impossible unless one is willing to spend a lot of money and accept some limitations.
Here are the general formulas I use when doing tech support and helping customers with their sine wave generation.

PeakVelocity=Amplitude\cdot 2\pi Hz
PeakAcceleration=Amplitude\cdot { \left( 2\pi Hz \right) }^{ 2 }
so the peak acceleration of a 100 Hz sine wave with an amplitude of 1mm is
0.001m\cdot { \left( 2\pi \frac { 100 }{ s } \right) }^{ 2 }=394.784\frac { m }{ { s }^{ 2 } } =40.257g
This very acceleration rate will be difficult to achieve. The natural frequency of the cylinder and load must be higher than 100 Hz and so must the frequency of the valve. If the actual position does not need to follow the target position, the RMC can be used to generate a 100 Hz sine wave and the amplitude of the signal from the RMC can be increased to increase the amplitude of the sine wave but the gain will be very low so the amplitude will not be very high. When simply generating a pure sine wave signal one most use a symmetrical cylinder or the cylinder will tend to move in the extend direction over time.