WS10Key - 3. Yes, 2 y 1 is always a solution of the second...

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Math 224, Spring 2007, Quiz/Worksheet 10 Name: Use the front and back of this sheet to complete the following problems. If additional paper is needed, staple the extra sheet to this one. Complete the following problems from the text. 1. Chapter 4 Review Exercises #2 2. Chapter 4 Review Exercises #6 3. Chapter 4 Review Exercises #12 4. Chapter 4 Review Exercises #20 1. Resonance occurs when the forcing frequency ω is the same as the natural frequency of the harmonic oscillator, Im ( λ ) = 2 i 2. No, solutions of first order DEs do not oscillate and therefore do not have resonance. General solution y ( t ) = ke - t + A cos( ωt ) + B sin( ωt ) is bounded.
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Unformatted text preview: 3. Yes, 2 y 1 is always a solution of the second equation. y 2 = 2 y 1 , y 2 = 2 y 1 , y 00 2 = 2 y 00 1 y 00 2 + y 2 + 4 y 2 = 2 y 00 1 + 2 y 1 + 4(2 y 1 ) = 2( y 00 1 + y 1 + 4 y 1 ) = 2 cos(3 t ) 4. y 00-y-6 y = 6 t + 3 e 4 t s 2-s-6 = 0 s = 3 ,-2 y h ( t ) = k 1 e 3 t + k 2 e-2 t y p = At + B + Ce 4 t y p = A + 4 Ce 4 t y 00 p = 16 Ce 4 t 16 Ce 4 t-( A + 4 Ce 4 t )-6( At + B + Ce 4 t ) = 6 t + 3 e 4 t-6 A = 6 A =-1-A-6 B = 0 B = 1 6 16 C-4 C-6 C = 3 C = 1 2 General solution y ( t ) = k 1 e 3 t + k 2 e-2 t-t + 1 6 + 1 2 e 4 t...
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This homework help was uploaded on 04/08/2008 for the course MATH 224 taught by Professor Hahn during the Spring '07 term at Case Western.

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