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Unformatted text preview: = mg (with g = 9 . 8 m/s 2 ) of the machine depresses the pad exactly 0 . 5 cm. When its rotor spins at radians per second, the rotor exerts a vertical force F o cos ( t ) newtons on the machine. At what speed (in revolutions per minute) will resonance vibrations occur? Exercise 25 : Show that t and t 2 are linearly independent on 1 < t < 1; indeed, they are linearly independent on every interval. Show also that W ( t, t 2 ) is zero at t = 0. What can you conclude from this about the possibility that t and t 2 are solutions of the equation y + p ( t ) y + q ( t ) y = 0? Verify that t and t 2 are solutions of t 2 y 2 ty +2 y = 0. Does this contridict your conclusion? Does the behavior of the Wronskian of t and t 2 contradict Abels theorem? Due Date: Wednesday, October 28 in class...
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 Spring '08
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 Math

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