Conservation of energy I think

AI Thread Summary
The discussion focuses on analyzing the motion of a bead on a vertical spring, emphasizing the need to demonstrate that the bead experiences a restoring force proportional to x^3 for small displacements. The user attempts to relate the problem to pendulum dynamics and considers the restoring force as kx. However, they express difficulty in progressing beyond this point and suggest drawing a free body diagram to identify the forces acting on the bead at displacement x. The conversation highlights the importance of understanding energy conservation principles in this context. Overall, the thread seeks clarity on the relationship between displacement and restoring force in spring dynamics.
Benevelli
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Homework Statement


PLEASE HELP: A bead at the end of a vertical spring moves without friction along a horizontal wire. WHen the spring is perfectly vertical , the spring is neither stretched or compressed. Show that the bead experiences a restoring force, and that if x is small, then the magnitude of the force is proportional to x^3 rather x^1. You will want to use the approximation (1+x)^n = 1+nx for x<<1

Homework Equations


U + K = E

The Attempt at a Solution


I tried thinking about this like a pendulum with kx as the restoring force. Other than that, my work has gotten me nowhere.
 
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Draw a free body diagram for the bead at some displacement x. What are the forces on it?
 

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