Can someone suggest a nice engineering application of a second order differential equation?

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I am writing a case for one of applied mathematics course involving solving differential equations. Can someone suggest an engineering application of a practical problem that I can ask my students to come up with a solution. Should not be as heavy as a heat equation nor should it be as easy of a simple first order differential equation. I am looking for moderate complexity. Even if someone suggests references that will be great.

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I would just like to point you to a great pdf that I found only recently that has exactly what you ask:

http://www.stewartcalculus.com/data/CALCULUS%20Concepts%20and%20Contexts/upfiles/3c3-AppsOf2ndOrders_Stu.pdf