Calculating Energy Stored in a Two-Spring System

[Skuzzy]

Homework Statement

A particle (4m) is suspended from a fixed point by a spring of stiffness k and natural length l₀. An identical 2nd spring is attached to this particle, and a mass (3m) is attached to its end. The system hangs vertically in equilibrium.
Take the datuim of P.E. a in each spring to be the natural length of that spring.

http://img176.imageshack.us/img176/2653/2springsytem.jpg

Write down the an equation for the energy stored in the two springs.

Homework Equations

The Attempt at a Solution

Spring 1, exerts force H₁=k(x₁-l₀)i

it supports both particles so W₁=7mgi

Spring 2, exerts force H₂=k(x₂-l₀)i

it supports only the lower particle so W₂=3mgi

The energy function U(x) = - -\int(F(x)) dx

I don't know how to proceed: Should I be integrating 2 equations for the force? Don't I need 'x' in F(x) to be the same in both cases? Have I just got myself in a muddle and am thinking about this all the wrong way?

Any help appreciated.

Homework Statement

Homework Equations

The Attempt at a Solution

 

[kuruman]

Can you find how much energy is stored in a spring if it stretches by amount x?
Can you find how much a spring stretches by if you hang mass m from it?
The bottom spring has mass 3m hanging from it.
The top spring has mass 7m hanging from it.

Put it together.

 

[Skuzzy]

I managed to make this way more complicated for myself than it needed to be... thanks for the help.

i had been trying to come up with a single equation but with two unknown extensions i was getting myslef in a quite a muddle.

SOLVED. thanks.