Chapter 8 Part II

# Chapter 8 Part II - SECTION 8.4 Laplace Transforms II 647...

This preview shows pages 1–4. Sign up to view the full content.

SECTION 8.4 Laplace Transforms II 647 8.4 Laplace Transforms II ! Stepping Out 1. The function first has the value of 0 for t < 0, then a from 0 to 1. Hence we write this as ft a t () = () step . However, at t = 1 the function shifts from a to b . We, therefore, subtract a and add b , yielding t b a t +− step step 1 . Finally, when t = 2, the function shifts from b to c , so we subtract b and add c . Thus for all t 0 we have t t c b t step step step 12 . 2. Following the procedure in Problem 1, we write the function as ft e t e t tt =+ − 11 2 2 3 bg b g step step . 3. Following the procedure in Problem 1, we write the function as t t t t =+ − − +− + 14 1 1 14 4 22 step step . 4. Following the procedure in Problem 1, we write the function as t t t t =− −− sin sin ππ step step 24 . ! Geometric Series 5. t t t + step step step 123 ! , L e s e s e s e s ee e s e e sss s ss s s s {} =+ + + = + + + += F H I K 23 1 1 1 !! afaf af ns . 6. t t t + 2 3 step step step ! , L s e s e s e e se s s =+ + + + = + + + + = F H I K 1 1 a f a f a f . 7. t t t 1 1 2 1 1 4 2 1 8 3 step step step ! , L s e s e s e e s e e s e e e s s s s s s s s s mr di =− − − = + F H G I K J + F H G I K J + F H G G I K J J R S | T | U V | W | F H G I K J F H G I K J = 1 248 1 1 2 1 1 1 2 1 1 1 1 2 21 2 2 1 2 .

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

View Full Document
648 CHAPTER 8 Forced Equations and Systems 8. ft t t () =− +− 11 2 step step ! , L s e s e s e ss e sss s {} =− + − = + F H I K −− 1 1 23 ! . 9. t t 12 1 2 2 step step ! , L s e s e s e e s ee s e se s s s + − =− − + + F H I K 2 2 1 1 1 2 !! a f di . ! Piecewise-Continuous Functions In the following problems we use the alternate delay rule LL t c e ft c cs =+ step kp . 10. The function can be represented by ft t t t t t t () = step step step step 1 2 . Using the delay rule we get L L s et e t e t e s e s e s e s e e s e s s s s s s s s + = −+− + + = + −−− 1 1 1 1 1 1 1 2 2 22 2 2 2 2 2 2 2 af . 11. t t tt bg b g ch − + − F H G I K J 3 13 step step step , L s e s e t e t s s e s e s s s mr R S T U V W R S T U V W + 2 1 2 3 3 . 12. t t t t 3 2 3 step step step , L e t e t e s e s e s e s e s e s e s s s s = −+ += −+= 3 3 2 3 2 33 2 3 2 2 2 2 2 . 13. ft b t a ta F H I K sin π 1s t e p a f , L L b t a be a b s be t a b s e as a a as a a as = F H G I K J R S T U V W + F H G I K J R S | T | U V | W | = + R S T U V W = + + sin sin sin . 2 2 2 2 1 14. t t F H I K sin 2 1 2 step step step a f , L s se e s e s s = + F H G I K J F H I K 1 2 2 2 2 2 b f .
SECTION 8.4 Laplace Transforms II 649 15. The two parts of the sine function can be written as ft t t t t t () =− −− sin sin ππ af a f a f 11 2 1 2 step step step , LL L L L t e t e t e t ss e s e s e s ee sss s s s bg mr lq ch ns di + + + + = + + + + + + + = + ++ −−− sin sin sin sin .

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

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

## This lab report was uploaded on 04/04/2008 for the course APPM 2360 taught by Professor Williamheuett during the Fall '07 term at Colorado.

### Page1 / 41

Chapter 8 Part II - SECTION 8.4 Laplace Transforms II 647...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online