The system in the figure below consists of a massless spring with stiffness 60 N/m and unstretched length 0.4 m (indicated in black in the figure) that is wrapped around a rigid massless bar (indicated in red in the figure). A mass of 5 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 qi the angle of the bar w.r.t. the vertical and as generalised coordinate q2 the stretch of the spring.
The system in the figure below consists of a massless spring with stiffness 60 N/m and unstretched length 0.4 m (indicated in black in the figure) that is wrapped around a rigid massless bar (indicated in red in the figure). A mass of 5 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 qi the angle of the bar w.r.t. the vertical and as generalised coordinate q2 the stretch of the spring.
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Derive the mathematical expressions for the position of velocity vectors of the mass in terms of the generalised coordinates q1 and q2.
Calculate the kinetic energy, potential energy and Lagrange functions of the system.
Transcribed Image Text:The system in the figure below consists of a massless spring with stiffness 60 N/m and
unstretched length 0.4 m (indicated in black in the figure) that is wrapped around a
rigid massless bar (indicated in red in the figure). A mass of 5 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 q1 the angle
of the bar w.r.t. the vertical and as generalised coordinate q2 the stretch of the spring.
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