Hi(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

Look at the drawing. Furthermore I have a constant acceleration [tex] \vec g = -g \hat y[/tex]

I shall find the Lagrange function and find the equation of motion afterwards.

2. Relevant equations

Lagrange/ Euler function and eqauation

3. The attempt at a solution

I found out the following for the kinetic energy and the potential energy:

[tex] T=\frac {1} {2} m_{1} \dot{\vec r_{1}}^{2} + \frac {1} {2} m_{2} \dot{\vec r_{2}}^{2}[/tex]

and for the potential energy:

[tex] V=\frac 1 2 k_{1}{\vec r_{1}}^{2}+\frac 1 2 k_{2} {\vec r_{2}}^{2}+m_{1}gy_{1}+m_{2}gy_{2}+\frac 1 2 k_{3}({\vec r_{1}}-{\vec r_{2}})^{2}[/tex]

Now I used the Euler- Lagrange equation of motion and found out that:

[tex] m_{1}\ddot{\vec r_{1}}=-k_{1}{\vec r_{1}}+k_{3}{\vec r_{1}}-m_{1}g\hat y[/tex]

and

[tex] m_{2}\ddot{\vec r_{2}}=-k_{2}{\vec r_{2}}-k_{3}{\vec r_{2}}-m_{2}g\hat y [/tex]

Can anyone confirm this? Or did I do any mistakes?

Thanks for your help

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Lagrange equation (2 masses, 3 springs)

**Physics Forums | Science Articles, Homework Help, Discussion**