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include the stretch of the spring own weight in potential energy for spring pendulum?

we are given a problem with spring with its own mass $m$. I am confused how to set up the PE term in the Lagrangian. Assume the spring has length of $L_{0}$ when it is laying on a table horizontally. ...
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182 views

The Gravity Spring [closed]

This problem examines the scenario of a tunnel drilled through the center of the Earth, and the length of time required for an object to fall through the hole and back again. use trigonometry to ...