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hw8_ocw - velocity Ω = 4 rad/sec but the pendulum is free...

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˙ ˙ 16.61 Handout #8 Prof. J. P. How April 10, 2003 Prof. J. Deyst Due: April 17, 2003 16.61 Homework Assignment #8 1. The equations of motion of the mass on the spring pendulum in problem #1 of HW#4 are given by: r 2 θ ¨ + 2 ˙ 2 cos θ ( d + r sin θ ) = g sin θ (1) k r ¨ r ( θ ˙ 2 + Ω 2 sin 2 θ ) + ( r r 0 ) = g cos θ + d 2 sin θ (2) m Assume that m = 1, k = 2, r 0 = 1 is the undeflected length of the spring and r (0) = 2, r (0) = 0, θ (0) = 0 , θ ˙ (0) = 0 . 1. Use the techniques discussed in class (ODE45) to solve these equations of motion numerically for r ( t ) and θ ( t ). The arm attached to the rotating shaft has length d = 0 . 8m, as shown in the figure. The shaft is rotating with a constant angular
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Unformatted text preview: velocity Ω = . 4 rad/sec, but the pendulum is free to Look at page 6–8 of the notes. Please submit all codes for this problem by email. 2. Show that a thin disc thrown up spinning about its major axis with a small nutation angle will make two wobbles to every cycle of spin. Try it- is it true? 3. Do problem 18.66 from Beer and Johnston Vector Mechanics for Engineers . 1...
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