Answer Happy

The system in the figure below consists of a massless spring with stiffness 30 N/m and unstretched length 0.3 m (indicated in black in the figure) that is wrapped around a rigid massless bar (indicated in red in the figure). A mass of 6 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 qı the angle of the bar w.r.t. the vertical and as generalised coordinate 42 the stretch of the spring. a) Derive expressions for the position an velocity vectors of the mass in terms of the generalised coordinates 91 and 92.
b) Determine the kinetic energy, potential energy and Lagrange functions of the system. c) Determine the Euler-Lagrange equations of the system. AT