Spring Mass Pulley System

math111

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

I will describe the problem as best as possible...
There is a Pulley with Radius [R]. There is a Mass as [M]. There is a Spring as [K]. The pulley has a Moment of Inetia [I]

The Mass is hanging in mid air by a string that goes straight up to the [left side] of the pulley. Then the string comes around to the [right side] of the pulley downwards. When it comes down there is a spring that is attached to the ground.


Derive the equation of motion using Lagrange equation?
2. Relevant equations

T ?
V ?
Lagrnage Equation
d/dt(Dt/D dot r1) - (DT/dr1)+(DV/dr1)

3. The attempt at a solution

T(kinetic)=1/2*M*xdot^2 +
V(Potential) = 1/2Kx^2