A student asked me how to find the time delay, for a second-order system by applying mathematical equation.
Let denote the final value of the waveform. Then, the rise time will be the time duration between to .
Since the time delay equals to the time for the waveform to reach . My rough idea for the mathematical equation is:
Just an approximation as the waveform between to is not a linear line.
2 thoughts on “Time Delay of An Underdamped Second Order System”
For an under-damped system, the rise time is the time it takes for the system to go from 0 to 100% of the final value