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Unformatted text preview: the damping coeFcient will make the system critically damped? 5. ind the Laplace transform. L { ( e t sin(3 t ) 000 } HINT: ( e t sin(3 t ) = e t sin(3 t ) + 3 e t cos(3 t ) ( e t sin(3 t ) 00 = ( 2 + 9) e t sin(3 t ) + 6 e t cos(3 t ) Page 4 of 8 MATH 251 2nd exam6. Find the solution to the following initial value problem. y 00 + 2 y8 y = e 3 t u 3 ( t ) , y (0) = 0 , y (0) = 1 Page 5 of 8 MATH 251 2nd exam7. Solve the initial value problem. y 00 + 5 y + 4 y = 2 ( t3) , y (0) = 1 , y (0) = 0 Page 6 of 8 MATH 251 2nd exam8. Find the general solution. ~x = 1 4 3 ~x, ~x = 7 . Page 7 of 8 MATH 251 2nd exam9. Find the general solution to the following systems of equations. (a) ~x = 13 3 1 ~x (b) ~x = 3 221 ~x Page 8 of 8...
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This note was uploaded on 07/23/2008 for the course MATH 251 taught by Professor Chezhongyuan during the Spring '08 term at Pennsylvania State University, University Park.
 Spring '08
 CHEZHONGYUAN
 Math, Differential Equations, Equations, Partial Differential Equations

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