A block of mass m is attached to a wedge of mass Mhby a spring of natural length lo andMaspring constant k. The inclined frictionless surfaceof the wedge makes an angle a to the horizontal. Thewedge is free to slide on a horizontal frictionless surface as shown in the figure.a) Write down all constraint relations on the particles? motion in cartesian coordinates.b) Show that the number s of degrees of freedom is 2 (.c) Choose s convenient generalized coordinatestd) Obtain the expression of the velocity of m with respect to O and show thatVm/o = xỉ + s7e) Take the reference of potential energy at Ox axisObtain the expression of the kinetic and potential energy (gravitational plus Elastic) ofthe system (wedge + block). (f) Show that the Lagrangian function is given by:(M + m)L =1ン?、+jms² + ma's'cos(a) – (s – lo) – mg(h – ssin(@))specifying the origin of each term in the Lagrangian functio.g) Obtain expressions of the generalized momentah) Derive the Euler - Lagrange equations (

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