# Lagrange's Equation of Motion

## Homework Statement

two blocks each of mass m are connected by an extensionless uniform string of length l. one block is placed on a smooth horizontal surface and the other block hangs over the side the string passes over a frictionless pulley. describe the motion of the system when the mass of the string is negligible

2. Relevant information, equations...
The only necessary equation you need to know is Lagrange's of Motion which states:

(i've tried putting in the partial signs but its not working out so i will have to type it out!)
partial L/partial q -(d/dt) partial L/partial q' + lambda (partial f/partial q)
where f is the equation of constraint, L is the langrange equation found from L=T-U, q is the variable of which you are taking a derivative, and lambda is the force of constraint

Attempt at a solution:
I know how to do work through the partial derivatives and plug in everything to get the equations of motion and all that, my only problem is finding an equation of constraint. From there, I have no problems. Any suggestions?

## The Attempt at a Solution

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gabbagabbahey
Homework Helper
Gold Member
Well, the string will be bent like this:

x
-----------
|
| y
|

Since the string is of Length L, I would say that for all values of x,y you have $x+y=L$...would you not agree?