Energy in a system of springs

**bobred** · April 29th 2010, 07:21 AM

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

Datum taken at point A,

Where

is kinetic energy and

is the spring stiffness and

is the natural length.

3. The attempt at a solution
By analysing the diagam
$U_{springA}=-\frac{1}{2}k(x-l_0)^2$

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

My question is, is the answer

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

**CaptainBlack** · April 29th 2010, 08:52 PM

Originally Posted by bobred

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

Datum taken at point A,

Where

is kinetic energy and

is the spring stiffness and

is the natural length.

3. The attempt at a solution
By analysing the diagam
$U_{springA}=-\frac{1}{2}k(x-l_0)^2$

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

My question is, is the answer

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

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