I need this answered please. A massless long, narrow tube is fixed to a horizont

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I need this answered please.

A massless long, narrow tube is fixed to a horizontal plane with a frictionless axle. A thin rod of mass M and length L slides without friction inside the tube. (40 points) A. Show that the moment of inertia of the rod about its center of mass is (1/12)"M"L2 B. Choose a suitable set of coordinates and write Lagrange's Equations for this system. C. Initially the rod is centered over the pivot and the tube is rotating at an angular velocity of wo. If it is disturbed slightly, what is the speed of the rod along the radial direction as a function of position? (Hints: consider conserved quantities and recall that x =--(x2) because 2 dx dx dt dt dt D. Find the radial and angular speed of the rod after a long time (assume the tube is infinitely long).

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