Using Lagrangian to derive the equation of motion

1. Feb 12, 2017

mmalon15

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

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

3. The attempt at a solution

sorry for the sideways picture... dont know why its doing that. but please help homework is due tomorrow morning! thanks!

2. Feb 12, 2017

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?

3. Feb 12, 2017

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 theres a onstraint of x = rθ

4. Feb 12, 2017

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.