wksht06

# wksht06 - MATH 152 L1& L2 Applied Linear Algebra and...

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

Unformatted text preview: MATH 152 L1 & L2 Applied Linear Algebra and Diﬀerential Equations Week 06 Worksheet (March 7, 2005): Laplace Transform Spring 2004-05 Q1. (Initial value problem) Consider the initial value problem (a) Show that L{y (t)} = s L{y (t)} − y (0). y − y = e2t , y (0) = 1. (b) Apply the Laplace transform to both sides of the given equation, and then determine L{y (t)}. (c) Apply the inverse Laplace transform to ﬁnd y (t) from L{y (t)}. Q2. (Inverse Laplace transform) Find the inverse Laplace transform of the following. (a) L−1 1 3s 2 +2 +2 2s + 1 s +4 s +4 (b) L−1 s+1 s2 + 6s + 10 (c) L−1 2s s2 − 4 (d) L−1 2s + 1 s2 − 2s + 5 (e) L−1 1 (s − 2)(s + 2)(s2 + 1) Q3. (Unit step function) Write the following function (or switch) in terms of unit step function. −5, 32, f (t) = 18, 11, if t < 4, if 4 if 7 if t t < 7, t < 28, 28. Q4. (Laplace transform of unit step function) Find the Laplace transform of each of the following. (a) f (t) = 10 u14 (t) + 2(t − 4)3 u4 (t) − (5 − e12−4t ) u3 (t). (b) g (t) = t, −8 + (t − 6) , 2 if t < 6, if t 6. Q5. (Inverse Laplace transform) Find the inverse Laplace transform of F (s) = e−4s . s(s2 + 4) Q6. (Initial value problem) Find the solution of the initial value problem where h(t) = 0, 3, if t < 4, if t 4. y + 4y = h(t), y (0) = 0, y (0) = 0, ...
View Full Document

## This note was uploaded on 09/30/2010 for the course MATH MATH152 taught by Professor Kcc during the Spring '10 term at HKUST.

### Page1 / 2

wksht06 - MATH 152 L1& L2 Applied Linear Algebra and...

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

View Full Document
Ask a homework question - tutors are online