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I'm a mechanical engineering major/electrical engineering minor university student. A huge part of mechanical and electrical engineering is control theory, which I enjoy immensly. I have yet to take any ME control electives but took a systems/stability course as my last EE elective. The course consisted of a review of Laplace transforms, poles and zeros of transfer functions and how they relate to stability,routh criterion, forced and natural response, state space etc.

I understand the concept mathematically of why a critically damped step response is the ideal situation, but the one thing that always left me hanging was that I never understood how to interpret all of this theory physically. My professor always made a joke about systems that werent BIBO stable saying that "your plane has crashed" due to failure of the system.

My question is, what is the significance of poles, stability, step response, damping etc in the physical world? I understand how all of theory works, but I cannot explain how to use it.

Thank you!

KiltedEngineer