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I am a junior Mechanical engineering student with a midterm in my Vibrations I class on Thursday. I've been studying but I'm having some issues really nailing the concepts fundamentally. I feel like I'm stuck in a rut of doing the problem like in the example, but not really understanding what it is that I'm doing.

The two main subjects on this exam are the modeling of vibratory systems and finding governing equations for single degree-of-freedoms systems. Specifically, we've learned a method for representing vibratory systems as circuits, finding equivalent stiffness k for each element and adding them up in series and parallel for the first topic, and using the force-balance method and Lagrange's equations for the second topic.

So my request is for materials. Does anybody know of any resources (online I prefer, but I can get to the library tomorrow if I need to so engineering textbooks might work too), that:

1) Show a lot of examples of this circuit modeling process? My textbook is short on examples and my professor is big on the school of "Don't work out problems and don't give solutions."

2) Explain the Lagrange process? I understand the force-balance method. That makes sense physically. But for the Lagrange I see a lot of math and it's not physically making sense to me.

Thanks a lot for all of your help! Of course, if any of you feel up to explaining Lagrange to me, that would be great too... But honestly any good material anyone has come across would be amazing, because I really have no clue where to start.

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# Reference Material for Undergraduate Level Vibrations Courses

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