[Math] How to tell the difference between 1st order response and 2nd order response

calculus

Apologies, not sure where to tag this but If one were to look at a graph and see a response to a step input change, how does one know the difference between a 1st order response and a 2nd order response? one can easily spot an underdamped response straight away, but 1st order response, critically damped and overdamped response all look so similar, is there a key to determining this from a graph?

1st order response
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2nd order response
enter image description here

Best Answer

If the curve has an inflection point, then the system is second order. Otherwise, I am afraid that there is little you can do.