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Unformatted text preview: ECE360 EXAM #3 FALL 2007 Instructions : 1. Closedbook, closednotes, openmind exam. 2. Work each problem on the exam booklet in the space provided. 3. Write neatly and clearly for partial credit. Cross out any material you do not want graded. 4. Leave one empty seat between each of you. Name : Problem 1 : /25 Problem 2 : /25 Problem 3 : /20 Problem 4 : /30 Total : /100 1 Problem 1 (25 Points) 2 M 1 M θ L L The above figure shows a pendulum made of a massless rigid rod linking two masses M 1 and M 2 located at distances L and 2 L from the pivot of the pendulum. The pendulum is given initial conditions θ (0) 6 = 0 and ˙ θ (0) = 0. (a) Write the total and constant energy deviation of the system ∆ E as a function of θ and ˙ θ . (b) Show the pendulum angle θ ( t ) is governed by the following nonlinear secondorder differential equation: ( M 1 L 2 + 4 M 2 L 2 ) ¨ θ + ( M 1 + 2 M 2 ) gL sin θ = 0 (c) Assuming that M 1 = M 2 = M and θ (0) is small enough so that sin θ ( t ) ∼...
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 Spring '08
 STAFF
 sin θ, secondorder differential equation, Magnetic levitation System

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