Properties differentiation theorem df t sf s

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: + βF2 (s) Example: y( t ) = 2a ( t ) + 3b( t ) Y(s) = ? Properties Differentiation Theorem df ( t ) = sF ( s ) − f (0) dt d 2 f (t) = s 2 F ( s ) − sf (0) − f (0) 2 dt n d n f (t) n = s F ( s ) − ∑ s n − k f k −1 (0) n k =1 dt Properties E xa m p le : dy (t ) + 3 y (t ) = 0 dt y (0) = 3 d 2 y (t ) dy (t ) + 12 + 32 y (t ) = 32u (t ) 2 dt dt y (0) = y ' (0) = 0 Properties Fina l Va lue T h e o re m (FVT ) lim f ( t ) = lim sF(s) t →∞ s →0 This theorem applies, if and only if, all poles of sF(s) lies in the left half s plane. Example. Find f(∞ ) for the following system 1 F (s) = s ( s + 1) Inverse Laplace Transform The Inverse Laplace transformation for a function F(s) is σ + j∞ 1 st f (t ) = F ( s )e ds ∫j∞ 2πj σ − However, the inversion integral is complicated. A convenient method for obtaining inverse Laplace transform is to use a table of Laplace transform. 3 f (t ) = ? F ( s) = s+4 Inverse Laplace Transform Partial fraction expansion method can be used to find the inver...
View Full Document

Ask a homework question - tutors are online