A thin rod of mass m and length L swings from a spring of stiffness k...

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A thin rod of mass m and length L swings from a spring of stiffness k and unstretched length L In addition to gravity, there is a force P that is applied at end B of the rod such that the force is always perpendicular to the rod. The entire system can be considered to move in a two- dimensional vertical plane. We wish to model this system using the generalized coordinates q₁ = r, q2 = 01, and q3 = 0₂. (a) (8 points) Find the kinetic energy expression for this system. (b) (5 points) Find an expression for the potential energy of the system (c) (7 points) Give expressions for the virtual work and the generalized forces Q1, Q2, and Q3. (d) (5 points) Give the full equation of motion for the 1st generalized coordinate, q1 = r(t). A m, L B P A thin rod of mass m and length L swings from a spring of stiffness k and unstretched length L In addition to gravity, there is a force P that is applied at end B of the rod such that the force is always perpendicular to the rod. The entire system can be considered to move in a two- dimensional vertical plane. We wish to model this system using the generalized coordinates q₁ = r, q2 = 01, and q3 = 0₂. (a) (8 points) Find the kinetic energy expression for this system. (b) (5 points) Find an expression for the potential energy of the system (c) (7 points) Give expressions for the virtual work and the generalized forces Q1, Q2, and Q3. (d) (5 points) Give the full equation of motion for the 1st generalized coordinate, q1 = r(t). A m, L B P

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