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 ω radians per second, the rotor exerts a vertical force F o cos ( ω 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 Abel’s theorem? Due Date: Wednesday, October 28 in class...
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 Spring '08
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 Math, Force, Mass, Steady State, Department of Mathematical Sciences University of Delaware

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