Homogeneous 2nd Order DE from spring pendulum

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SUMMARY

The discussion centers on the derivation of motion equations for a spring pendulum using the Lagrangian equation in Classical Mechanics. The participant presents two second-order differential equations: y'' + x*y + g*cos(y) + k/m = 0 and y'' - (g*sin(y))/x = 0. The equations are questioned for their correctness, indicating a need for verification of the derivation process. The inquiry seeks clarification on whether these equations have a specific name or a known method for solving them.

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DavitosanX
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I'm currently taking a Classical Mechanics course, and we're studying the lagrangian equation. After a few exercises, I thought I'd try to come up with the motion equations for a pendulum where the mass hangs from a spring. The resulting differential equations take a form that I don't really know how to solve. They take the form:

y'' + x*y + g*cos(y) + k/m = 0

and

y'' - (g*sin(y))/x = 0

I would just like to know if these have a particular name, or maybe a specific method to solve them. Thanks for the help!
 
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You should check your derivation. The equations that you have don't look right.
 

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