Elliptic Pendulum: Homework on Kinetic & Potential Energies

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The discussion revolves around a physics homework problem involving a uniform rod attached to a slider, analyzing its kinetic and potential energies while swinging in a vertical plane. The student struggles with treating the rod as a continuum and deriving the correct expressions for kinetic energy (T) and potential energy (U). They mention the velocity equation and seek clarification on determining the x-coordinate of the center of mass. The conversation highlights the need for guidance in applying Lagrange's equations and ensuring the Lagrangian is regular. Overall, the thread emphasizes the challenges faced in solving complex dynamics problems in mechanics.
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Homework Statement



A uniform rod AB of mass M and length 2l attatched to a slider at A which is constrained to move along a smooth horizontal wire. The rod, which is subject to gravity, is free to swing in the vertical plane containing the wire. Using Ω (the angle between rod and vertical) and x coordinate of the centre of mass, find an expression for the kinetic and potential energies, deduce Lagrange's equations. Show that the Lagrangian is regular.



Homework Equations





The Attempt at a Solution


I know I have to treat the rod as a continuum, but I can't get around it...

Sorry it doesn't seem like I've done much but I've tried every way I know and nothing's working, any advice would be greatly appreciated. Thank you

Could you please start me of...I know v=-2lmcosθ

But to get T could you please help me... I don't know what my x coordinate is
 
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KE = 1/2[Mx.^2 + θ.^2 Ml^2 sin^2(θ)]

I have seemed to get this...could any1 please check if I have done this right
 

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