This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: MAP2302/2331 Exam3 Dr Sin No Calculators. Answer the questions in the spaces provided on the question sheets. Please write your answers in full detail. If you run out of room for an answer, continue on the back of the page. Name: 1. (7 points) Let L{ y ( t ) } ( s ) = Y ( s ). Find L{ e 3 t ty ( t ) } ( s ) . Be sure to explain clearly which general properties of the Laplace transform you use. Solution: By the t differentiation formula (5), we have L{ y ( t ) } ( s ) = sY ( s ) y (0) . Then by the s differentiation formula (6), L{ ty ( t ) } ( s ) = d ds ( sY ( s ) y (0)) = sY ( s ) Y ( s ) . Finally, by translation in t , L{ e 3 t ty ( t ) } ( s ) = ( s 3) Y ( s 3) Y ( s 3) . 2. (8 points) Find the Laplace transform F ( s ) of the function f ( t ) = cos 3 t, if 0 < t < π , if π < t . Solution: We can write use the step function to write f ( t ) = cos 3 t u ( t π ) cos 3 t....
View
Full
Document
This note was uploaded on 02/21/2010 for the course MAP 2302 taught by Professor Tuncer during the Spring '08 term at University of Florida.
 Spring '08
 TUNCER

Click to edit the document details