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homework2

# homework2 - Homework Assignment 2 Physics 302 Classical...

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Homework Assignment 2 Physics 302, Classical Mechanics Fall 2010 A. V. Kotwal Handed out: Friday, Sep. 10, 2010 Due in class on: Friday, Sep. 17, 2010 Problems 1. A double plane pendulum consists of a simple pendulum (mass m 1 , length l 1 ) with another simple pendulum (mass m 2 , length l 2 ) suspended from m 1 , both constrained to move in the same vertical plane. Write down the Lagrangian of this system in suitable coordinates, and derive Lagrange’s equations. 2. Consider a stretchable plane pendulum, i.e. a mass m suspended from a spring of spring constant k and unstretched length l , constrained to move in a vertical plane. Write down the Lagrangian and obtain the Euler-Lagrange equations. 3. A wire is bent into the shape given by y = A | x n | , n 2 and oriented vertically, opening upward, in a uniform gravitational field g . The wire rotates at a constant angular velocity ω about the y axis, and a bead of mass m is free to slide on it without friction. Find the equilibrium height of the bead on the wire. Consider especially the case

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