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

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: 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

Page1 / 2

wksht06 - MATH 152 L1 &amp;amp; L2 Applied Linear Algebra...

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