Review Problem 6 solution

# Review Problem 6 solution - -= Then use superposition to...

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6. What is the total response to ( ) ( ) 3 3 1 t u t e - = - when ( ) 0 .6 x = - and ( ) 0 1 x = dotnosp . We utilize our work from previous problems to solve this problem. From Problem 1, ( ) ( ) ( ) 0 0 2 2 2 2 5 2 5 U s s x x X s s s s s + + = + + + + + dotnosp . Next use superposition to decompose the problem into two parts. Rewrite the previous expressions as ( ) ( ) ( ) 1 2 X s X s X s = + where ( ) ( ) 1 2 2 5 U s X s s s = + + and ( ) ( ) 0 0 2 2 2 2 5 s x x X s s s + + = + + dotnosp . From Problem 2, ( ) 2 .6 cos2 .2 sin 2 t t x t e t e t - - = - + and from Problem 5 ( ) 3 1 3 3 9 27 cos2
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Unformatted text preview: --=---. Then use superposition to combine the solution of the two parts ( ) ( ) ( ) 3 1 2 3 3 3 cos2 9 sin 2 .6 cos2 .2 sin 2 5 8 t t t t t x t x t x t e e t e t e t e t-----= + =----+ . Combining terms yields ( ) 3 3 3 18 44 cos2 sin 2 5 8 5 5 t t t x t e e t e t---=---. Alternative solution forms are possible, but this is fine as is....
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