Answer Happy

Question 4 IF YOU USE SYMPY TO ANSWER THIS QUESTION, PLEASE ADD YOUR JUPYTER NOTEBOOK TO YOUR SOLUTIONS The system in the figure below consists of a massless spring with stiffness 40 N/m and unstretched length 0.1 m (indicated in black in the figure) that is wrapped around a rigid massless bar (indicated in red in the figure). A mass of 4 kg is attached to the end of the spring and slides without friction along the bar. The spring/bar assemblage pivots without friction about the point O. Take as generalised coordinate q the angle of the barw.r.t, the vertical and as generalised coordinate q2 the stretch of the spring, a) Derive expressions for the position an velocity vectors of the mass in terms of the generalised coordinates 1 and 42 b) Determine the kinetic energy, potential energy and Lagrange functions of the system. c) Determine the Euler-Lagrange equations of the system.