hw1_SOL

hw1_SOL - MAE 171a Homework Problem Set 1 Prof Schwartz Due...

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: MAE 171a Homework Problem Set 1 Prof. Schwartz Due: June 28th 1. Find the Laplace Transform of (a) f ( t ) = e- . 7 t cos(2 t ) Using transform number 15 ( L bracketleftbig e- at cos ωt bracketrightbig = s + a ( s + a ) 2 + ω 2 ) L bracketleftbig e- . 7 t cos(2 t ) bracketrightbig = s + 0 . 7 ( s + 0 . 7) 2 + 4 = s + 0 . 7 s 2 + 1 . 4 s + 4 . 49 (b) f ( t ) = t 3 e- at Using transform number 17 ( L bracketleftbig t n e- at bracketrightbig = n ! ( s + a ) n +1 ) L bracketleftbig t 3 e- at bracketrightbig = 6 ( s + a ) 4 (c) f ( t ) = t 1 ( t ) + ( t- 1) 1 ( t- 1)- 2 t 1 ( t- 1) where 1 ( t ) is the unit step function. First, rewrite f ( t ) so that f ( t ) = t 1 ( t )- ( t- 1) 1 ( t- 1)- 2 1 ( t- 1). Then it follows that L [ f ( t )] = 1 s 2- e- s s 2- 2 e- s s = 1- e- s- 2 se- s s 2 2. Find the Inverse Laplace Transform of (a) F ( s ) = 1 s ( s +2) = R 1 s + R 2 s +2 R 1 = lim s → 1 s + 2 = 1 2 R 2 = lim s →- 2 1 s =- 1 2 thus f ( t ) = 1 ( t ) 2 (1- e- 2 t ). This is a typical step response to a first order system. Note the effectiveness of the Final Value Theorem....
View Full Document

This note was uploaded on 02/02/2011 for the course MAE 107 taught by Professor Tsao during the Spring '06 term at UCLA.

Page1 / 4

hw1_SOL - MAE 171a Homework Problem Set 1 Prof Schwartz Due...

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