finalCrib - ENGI 5821 FORMULA SHEET FOR FINAL EXAM Modeling...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

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

Unformatted text preview: ENGI 5821 FORMULA SHEET FOR FINAL EXAM Modeling Laplace Transform: L{ f ( t ) } = F ( s ) = Z - f ( t ) e- st dt The Inverse Laplace Transform: L- 1 { F ( s ) } = 1 2 j Z + j - j F ( s ) e st ds = f ( t ) u ( t ) The Laplace Transform Pair Table: f ( t ) F ( s ) 1. ( t ) 1 2. u ( t ) 1 s 3. tu ( t ) 1 s 2 4. t n u ( t ) n ! s n +1 5. e- at u ( t ) 1 s + a 6. (sin t ) u ( t ) s 2 + 2 7. (cos t ) u ( t ) s s 2 + 2 Laplace Transform Theorems: Theorem Name 1. L{ f ( t ) } = F ( s ) = R - f ( t ) e- st dt Definition 2. L{ kf ( t ) } = kF ( s ) Linearity theorem 3. L{ f 1 ( t ) + f 2 ( t ) } = F 1 ( s ) + F 2 ( s ) Linearity theorem 4. L{ e- at f ( t ) } = F ( s + a ) Frequency shift theorem 5. L{ f ( t- T ) } = e- sT F ( s ) Time shift theorem 6. L{ f ( at ) } = 1 a F ( s a ) Scaling theorem 7. L{ df dt } = sF ( s )- f (0- ) Differentiation 8. L{ d 2 f dt 2 } = s 2 F ( s )- sf (0- )- f (0- ) Differentiation 9. L{ d n f dt n } = s n F ( s )- n k =1...
View Full Document

Page1 / 5

finalCrib - ENGI 5821 FORMULA SHEET FOR FINAL EXAM Modeling...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online