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Problem 4: The center of a long frictionless rod is pivoted at the origin, and the rod is forced to rotate in a horizontal plane with constant angular speed w. A bead of mass m is threaded on the rod. (a) Using the bead's distance from the pivot p as a generalized coordinate, write down the Lagrangian for the system. (b) Solve Lagrange's equation for p(t), in terms of initial conditions Po and vo p(0). [This system should look familiar to you from a previous problem set. 1

Problem 4: The center of a long frictionless rod is pivoted at the origin, and the rod is forced to rotate in a horizontal plane with constant angular speed w. A bead of mass m is threaded on the rod. (a) Using the bead's distance from the pivot p as a generalized coordinate, write down the Lagrangian for the system. (b) Solve Lagrange's equation for p(t), in terms of initial conditions Po and vo p(0). [This system should look familiar to you from a previous problem set. 1

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Problem 4: The center of a long frictionless rod is pivoted at the origin, and the rod is forced to rotate in a horizontal plane with constant angular speed w. A bead of mass m is threaded on the rod. (a) Using the bead's distance from the pivot p as a generalized coordinate, write down the Lagrangian for the system. (b) Solve Lagrange's equation for p(t), in terms of initial conditions po and vo p(0). [This system should look familiar to you from a previous problem set.] =
Transcribed Image Text:Problem 4: The center of a long frictionless rod is pivoted at the origin, and the rod is forced to rotate in a horizontal plane with constant angular speed w. A bead of mass m is threaded on the rod. (a) Using the bead's distance from the pivot p as a generalized coordinate, write down the Lagrangian for the system. (b) Solve Lagrange's equation for p(t), in terms of initial conditions po and vo p(0). [This system should look familiar to you from a previous problem set.] =
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