How Do You Calculate the Energy Stored in a Nonlinear Spring?

AI Thread Summary
To calculate the energy stored in a nonlinear spring described by the force equation F = -kx - cx^3, where k = 233 N/m and c = 4.0 kN/m^3, the appropriate method involves integrating the force over the displacement. The energy stored in the spring can be determined using the equation Us = (1/2)kx0^2 - (1/2)kx_f^2, but adjustments are needed due to the nonlinear term. An integration approach is necessary to account for the cubic term in the force equation, which complicates the calculation. The initial attempts to directly substitute values into the energy equation were incorrect, highlighting the need for proper integration to find the energy stored. Understanding the relationship between force and energy in nonlinear systems is crucial for accurate calculations.
Charanjit
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1. Homework Statement

The force exerted by an unusual spring when it's compressed a distance 20cm from equilibrium is given by F= -kx-cx3, where k= 233 N/m and c= 4.0kN/m3

Question: Find the energy stored in this spring when it's been compressed 20cm.



2. Homework Equations
Equation already given, I think we supposed to use that one. But the equation of spring constant is Us= (1/2)kx02-(1/2)kxf2.



3. The Attempt at a Solution .
I actually just put in the right numbers in the equation given, but was incorrect. Did integrate the function, and was wrong. No clue what to do.
 
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Force doesn't equal energy. Hope that helps haha :)
 

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