# 40 Transient Response of Mechanical Systems

For most sensor applications in mechanics you can solve transient response problems with money. Buy a better sensor with a higher natural frequency to follow the fastest transients in your system. Alternately, filter the output of your slower sensors to eliminate transients approaching the natural frequency if you are mostly interested on mean values. Courses in Dynamics and Vibrations will give you a much deeper background in the differential equations of transient mechanics.

# The Math Behind Second Order Response

All systems with moving mass in them follow a second order response model with time because the acceleration term in F=ma is a second derivative of position. If they are not heavily damped (not much friction) then they will oscillate or vibrate when subjected to a sudden change. The load cell in the MECH 217 lab will show that behaviour and make our measurements difficult.

A diaphragm pressure transducer can be described with a simple 1D mass-spring-damper model to approximate dynamic response close to the real thing. Getting actual values for stiffness and damping are much more difficult, although we can measure them indirectly. (video 7:54)

## Getting from Performance Data to a Model

We can match a second order model to the response we observe to a step change in pressure. We don’t need to know the details of the transducer in order to get a mathematical model that provides a good approximation for natural frequency and damping. Then we can use that model to predict more complicated cases, and we can apply this approach to just about any system with an oscillating mass in it. (video 12:17 follow along using the Python Learning Sequence example 7.3)

## License

Rick's Measurement for Mechatronics Notes Copyright © 2019 by Rick Sellens is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License, except where otherwise noted.