# Math Help - Energy in a system of springs

1. ## 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

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

2. 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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CB