Solving Spring Force Problems: Showing Maximum Displacement & Velocity

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SUMMARY

The discussion focuses on solving a spring force problem involving a non-ideal spring with a force defined by F = zx², where x is the displacement from the equilibrium position and z is a constant. The maximum downward displacement of a mass m attached to the spring is derived to be (3mg/z)^(1/2). Additionally, the problem requires determining the displacement at which the mass achieves its maximum velocity, emphasizing the importance of calculating spring potential energy as a function of displacement.

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I'm just having some trouble with this problem. Any help would really be appreciated. I'm not even sure where to start.

A spring (not ideal) supplies a force given by F = zx^2, where x is measured from the equilibrium position and z is a constant. A mass m is attached to the spring and then released from rest at x = 0 (non-stretched spring)

a) show that the maximum downward displacement of the mass will be (3mg/z)^(1/2)
b) At what displacement will the mass have its maximum velocity

Thank you
 
Last edited:
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Start by deriving the spring potential energy as a function of displacement x. (Hint: How much work is required to stretch the spring?)
 

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