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

[Charanjit]

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 U_s= (1/2)kx₀²-(1/2)kx_f².



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.

 

[Nebozilla]

Force doesn't equal energy. Hope that helps haha :)

 

[kerimek]

I would suggest approaching this problem by using the equation for potential energy of a spring, which is Us = (1/2)kx^2. In this equation, k represents the spring constant and x represents the displacement from equilibrium.

In this problem, we are given the values for k and x, so we can plug them in and solve for the potential energy stored in the spring.

Us = (1/2)(233 N/m)(0.20 m)^2
Us = 4.66 J

Therefore, the energy stored in the spring when it is compressed 20cm is 4.66 Joules.

It is important to note that the given equation, F= -kx-cx^3, is the equation for the force exerted by the spring, not the potential energy. It is not necessary to integrate this function to find the potential energy. Additionally, the given equation for potential energy, Us= (1/2)kx02-(1/2)kxf2, is incorrect and does not match the equation given for the force.