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Unformatted text preview: t ): ( D 2 + 4 . 3 D + 31 I ) θ = f ( t ) where f is an additional forcing function. In addition there are initial conditions θ (0) and θ (0). (a) If f ( t ) = A sin ωt , what numerical value of ω would be the resonant frequency? (b) If you wanted the pendulum to more quickly adjust itself to another driving frequency ω 1 (not the resonant one), what would you change in the equation? 1 8. Given the matrix: A = ± i 4 i 1 + 4 i ² decompose it as A = H + X , where H is a Hermitian matrix and X is skewHermitian. 9. Find a general solution of x 2 y 003 y = 0 10. Can the following matrices be diagonalized? Answer without diagonalizing! Q = ± 3 2 3 6 ² R = ± 5 1 1 5 ² T = ± 5 1 5 1 ² 2...
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This note was uploaded on 07/23/2008 for the course MATH 405 taught by Professor Belmonte during the Fall '06 term at Pennsylvania State University, University Park.
 Fall '06
 BELMONTE
 Math, Calculus

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