Derive the kinetic energy of a mass on two springs

[ramialsaiad]

Homework Statement

Hi

I want to derive the equation of kinetic energy for a mass on two springs .. Here is the figure of the system:
http://faculty.ndhu.edu.tw/~clcheng/class-98/gen-phy98/gen-phy98-1-Q2s.pdf

Am I doing right for calculating the kinetic energy for the mass on two springs ?

Homework Equations

ΔK = ∫ F(x) · dx

The Attempt at a Solution

My attempt to solve the kinetic equation is by using this formula :

ΔK = ∫ F(x) · dx

so ΔK = (-2kx^2)/2 + ∫ 2kxL/(√(x^2 + L^2)) = (-2kx^2)/2 + 2kL*√(x^2 + L^2)

Am I doing right for calculating the kinetic energy for the mass on two springs ?

Thanks

 

[Andrew Mason]

Hi Ramialsaiad,

What are the limits for your integral?

You have to integrate between, say, x₀ and x. To determine the actual KE at a given point you would need to start at the value for x₀ where KE = 0.

AM