# Homework Help: Lagrangeian problem

1. Feb 10, 2010

### clueless_rosh

lagrangeian problem....

1. The problem statement, all variables and given/known data
in a spring pendulum system the spring is initially in equilibrium at upright position with theta = 0 and elongation (mg)/k, (k is spring constant). total length of spring in equilibrium condition is a with respect to which we define additional deviations in terms of a variable r. write dwn the lagrangian for this system

2. Relevant equations

L = kinetic energy - potential energy
kinetic energy = 0.5 mv^2
potential = mgh

3. The attempt at a solution
i know that the l = kinetic energy - the potential energy...but not exactly sure how to form my equations..please help...

i think potential energy would be 0.5(k*x^2) ?

Last edited: Feb 10, 2010
2. Feb 10, 2010

### Altabeh

Re: lagrangeian problem....

The first thing here is picturing the whole problem schematically! So graph the pendulum with given data and show it to us!

AB

3. Feb 10, 2010

### clueless_rosh

4. Feb 10, 2010

### clueless_rosh

Re: lagrangeian problem....

ok from what i can guess

potential energy = mgrcos(theta) - 0.5k*(r^2)
kinetic energy = 0.5(m(dr/dt)^2) + 0.5(mr^2)(dtheta/dt)^2

5. Feb 10, 2010

### Altabeh

Re: lagrangeian problem....

You got it right!

AB

6. Feb 10, 2010

### clueless_rosh

Re: lagrangeian problem....

ok thnx.. :)