PracticeProblemsMidterm_solu

# Let a system with input u and output y be represented

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: nswer is A, E, F, G 7. Let a system with input u and output y be represented by transfer function P (s). Suppose P (s) = 2 , s+3 u ( t) = 1 + e t . What is y (t)? Solution: U (s) = 1 1 + , s s+1 Y (s) = P (s)U (s) = 2 s+3 ✓ 1 1 + s s+1 ◆ = c1 c2 c3 + + , s s+1 s+3 where c1 = sY (s)|s=0 = 2 , 3 c2 = (s + 1)Y (s)|s= 1 = 1, Taking the inverse Laplace transform of Y (s), we have y ( t) = 1 (2 + 3e 3 t 5e 3t ) 2 c3 = (s + 3)Y (s)|s= 3 = 5 . 3 8. Sketch y (ty (in in the previousSketch y (t) in the previous problem. 8. Sketch ) t) the previous problem. 8. problem. Solution: Solution: Solution: LetLet the three terms in t) t) be denoted byterms and(C), be denoted by A, B , and C , the three terms in y (y ( be Let the threeAABBandy t, denoted by , , , , in C A+B where A is the ﬁrst term andwhere A islast. ﬁrst term and C is the last. Then each C is the last. Then each where A is the ﬁrst term and C is the theThen each y(t) 1 term can sketched as shown on the sketched as term can be be sketched as showncan...
View Full Document

## This note was uploaded on 01/27/2014 for the course MAE 171A taught by Professor Idan during the Winter '09 term at UCLA.

Ask a homework question - tutors are online