This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: the damping coeFcient γ will make the system critically damped? 5. ±ind the Laplace transform. L { ( e πt sin(3 t ) 000 } HINT: µ ( e πt sin(3 t ) = πe πt sin(3 t ) + 3 e πt cos(3 t ) ( e πt sin(3 t ) 00 = ( π 2 + 9) e πt sin(3 t ) + 6 πe πt 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 δ ( t3) , y (0) = 1 , y (0) = 0 Page 6 of 8 MATH 251 2nd exam8. Find the general solution. ~x = µ 1 4 3 ¶ ~x, ~x = µ 7 ¶ . Page 7 of 8 MATH 251 2nd exam9. Find the general solution to the following systems of equations. (a) ~x = µ 13 3 1 ¶ ~x (b) ~x = µ 3 221 ¶ ~x Page 8 of 8...
View
Full Document
 Spring '08
 CHEZHONGYUAN
 Math, Differential Equations, Equations, Partial Differential Equations

Click to edit the document details