{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Control ENG HW_Part_8

Control ENG HW_Part_8 - Y(t = i 4e −it − 1 4e −it...

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

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Y (t ) = i / 4e −it − 1 / 4e −it −1 / 4e it − 1 / 4te it Y (t ) = 1 / 4(ie − it − te −it − ie it − te it ) Y (t ) = 1 / 4(i (Cost − iSin t ) − t (Cost − i Sin t ) − i(Cos t + iSin t ) − t (Cos t + i Sin t ) ) Y (t ) = 1 / 4( 2 Sin t − 2t Cos t ) Y ( t ) = 1 / 2 ( Sin 3.8 f ( s) = = f ( s) = t − t Cos t) 1 s ( s + 1) 2 AB C ++ 2 s s s +1 = A( s + 1) + Bs( s + 1) + Cs 2 = 1 Let s=0 ; A=1 s=1; 2A+B+C=1 s=-1: C=1 B=-1 11 1 f ( s) = 2 + + s s s +1 f (t ) = (t − 1) + e − t PROPERTIES OF TRANSFORMS 4.1 If a forcing function f(t) has the laplace transforms f ( s) = = 1 e − s − e −2 s e −3s + − s s2 s 1 − e −3s e − s − e −2 s + s s2 f (t ) = L−1{ f ( s )} = [u(t ) − u(t − 3)] + [(t − 1)u (t − 1) − (t − 2)u (t − 2)] = u(t ) + (t − 1) u(t − 1) − (t − 2)u(t − 2) − u (t − 3) graph the function f(t) 4.2 Solve the following equation for y(t): t ∫ y (τ ) dτ 0 = dy (t ) y ( 0) = 1 dt Taking Laplace transforms on both sides t dy (t ) L{∫ y (τ ) dt} = L dt 0 1 . y ( s ) = s. y ( s ) − y (0) s ...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online