Using Lagrangian to derive the equation of motion

[mmalon15]

Homework Statement

derive the equation of motion of a mass-spring-pulley system using lagrange's equations. A mass m is connected to a spring of stiffness k, through a string wrapped around a rigid pulley of radius R and mass moment of inertia, I.

Homework Equations

kinetic energey
T = 1/2 (m)^(x_dot) + 1/2 (I)^(theta_dot)
potential energy
V = 1/2 k(R)^(x)

The Attempt at a Solution

sorry for the sideways picture... don't know why its doing that. but please help homework is due tomorrow morning! thanks!

 

[kuruman]

What is your Lagrangian? Without writing it down, you will not be able to derive the equations of motion.
It seems your generalized coordinates are x and θ. Is there a constraint relating the two?

 

[mmalon15]

ts the second to last equation on the picture, with the partial derivatives to the respect of x. so ∂T/∂x⋅ - ∂T/∂x + ∂V/∂x = Q

and i believe there's a onstraint of x = rθ

 

[kuruman]

That's not the Lagrangian. The Lagrangian is L = T - V. What you have is the equation for generalized coordinate x. You need to write another such equation involving θ and apply the constraint relating x and θ to get a single equation of motion.