Atwood machine probolem: Apply Lagrangian equations

[pentazoid]

Homework Statement

A uniform circular pulley of mass 2m can rotate freely about its axis of symmetry which is fixed in a horizontal position. Two masses m, 3m are connected by a massless string which passes over the pulley without slipping. The whole system undergoes planar motion with the masses moving vertically . Take the rotation angle of the pulley as generilesed coordinate and obtain Lagrange's equation for the mtoion. deduced upward acceleration.

Homework Equations

The Attempt at a Solution

3Mdv/dt=3Mg-T

Mdv/dt=T-Mg

deltaH=a*delta(theta)

v_c=v-a*omega

Sigma=T*dr=0

r x Mg(-y-hat)=0

pulley is frictionless.

Seems like the only thing I should do would be to find T which would help me find the acceletion for M.

 

[AEM]

Homework Statement

A uniform circular pulley of mass 2m can rotate freely about its axis of symmetry which is fixed in a horizontal position. Two masses m, 3m are connected by a massless string which passes over the pulley without slipping. The whole system undergoes planar motion with the masses moving vertically . Take the rotation angle of the pulley as generilesed coordinate and obtain Lagrange's equation for the mtoion. deduced upward acceleration.

Homework Equations

The Attempt at a Solution

3Mdv/dt=3Mg-T

Mdv/dt=T-Mg

deltaH=a*delta(theta)

v_c=v-a*omega

Sigma=T*dr=0

r x Mg(-y-hat)=0

pulley is frictionless.

Seems like the only thing I should do would be to find T which would help me find the acceletion for M.

Shouldn't you be constructing the Lagrangian which is given by

$$L = T - V$$

where T is the kinetic energy and V is the potential energy and from this you calculate the Euler-Lagrange equations?