A particle of mass m can slide freely along a light wire AB whose perpendicular distance...

 

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A particle of mass m can slide freely along a light wire AB whose perpendicular distance to the origin O is h. The line OC rotates about the origin at a constant angular speed . The position of the particle can be described in terms of the angle and the distance q to the point C. The initial conditions are 0 (0) = 0, q(0) = 0 and ġ(0) = 0. A y Ꮎ с 9 m mg x B (a) Using q as the generalized coordinate, find the Hamiltonian of the system. (b) Is the total mechanical energy given by the Hamiltonian? Is the total mechanical energy con- served? Explain. (c) Obtain equation of motion using Hamilton equation of motion. Solve for q(t). A particle of mass m can slide freely along a light wire AB whose perpendicular distance to the origin O is h. The line OC rotates about the origin at a constant angular speed . The position of the particle can be described in terms of the angle and the distance q to the point C. The initial conditions are 0 (0) = 0, q(0) = 0 and ġ(0) = 0. A y Ꮎ с 9 m mg x B (a) Using q as the generalized coordinate, find the Hamiltonian of the system. (b) Is the total mechanical energy given by the Hamiltonian? Is the total mechanical energy con- served? Explain. (c) Obtain equation of motion using Hamilton equation of motion. Solve for q(t).