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Energy in a system of springs

**1. Find the equation for conservation of energy in system. System consists of three springs A,B and C with stiffness k, 2k and 0.5k respectively and natural lengths l, 0.5l and 2l respectively.**

**2. Relevant equations**

Equation for conservation of energy http://www.physicsforums.com/latex_i.../2664029-0.png

http://www.physicsforums.com/latex_i.../2664029-1.png

Datum taken at point A, http://www.physicsforums.com/latex_i.../2664029-2.png

http://www.physicsforums.com/latex_i.../2664029-3.png

Where http://www.physicsforums.com/latex_i.../2664029-4.png is kinetic energy and http://www.physicsforums.com/latex_i.../2664029-5.png is the spring stiffness and http://www.physicsforums.com/latex_i.../2664029-6.png is the natural length.

**3. The attempt at a solution**

By analysing the diagam

$\displaystyle U_{springA}=-\frac{1}{2}k(x-l_0)^2$

$\displaystyle U_{springB}=-\frac{1}{2}*2k(x-\frac{1}{2}l_0-\frac{1}{2}l_0)^2=k(x-l_0)^2$

http://www.physicsforums.com/latex_i.../2664029-9.png

http://www.physicsforums.com/latex_i...2664029-10.png

http://www.physicsforums.com/latex_i...2664029-11.png

My question is, is the answer http://www.physicsforums.com/latex_i...2664029-12.png and have I derived the individual energies correctly?

Any help would be greatly appreciated, I've been banging my head against this for weeks.

James