For large displacements, and assuming rolling without slip, using LaGrange's principal, a) Find Velocity of the block and roller. Please use degrees of freedom shown in the picture. b) Find kinetic energy of the system c) Find potential energy of system ( Gravity is acting) d) Derive equations of motion of the system e) For small displacements, linearize equations of motion around their equilibrium positions. f) For small displacements, present equations of motion in a matrix form. g) Bonus: Find natural frequencies and mode shapes