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2.5 Solve ODE by Laplace Transform
Example
solution
& + 2 x + 10 x = 0
&
x
x(0) = 0
&
x(0) = 1
Laplace:
&
L [& + 2 x + 10 x ] = L [0]
x
s 2 X s sx(0) x(0) + 2[sX s x(0)] + 10 X s = 0
1
s 2 + 2s + 10
1
1
3
Xs =
=
( s + 1) 2 + 32 3 ( s + 1) 2 + 32
Xs =
PFE:
2.4 Inverse Laplace Transform
Definition
f (t ) = L1 [F ( s )]
1
Where: L
is called the Inverse Laplace Transform Operator.
How to do it?
F(S) is simple
use table of Laplace pairs
F(s) is complicated
Apply PFE first, then use table
PFE?
Partial Fraction
2.2 (b) Harmonic Motion
What is Harmonic Motion?
Consider a point Z, which moves along the circular orbit R with constant speed
Im (y)
z
R
t+
Re (x)
R radius of orbit or magnitude of Z (m or in.)
circular frequency (rad/s)
ZG2005
initial phase angle (r
Chapter 2 The Laplace Transform
Objective: Mathematical preparation for the study of next chapters
Contents:
2.1 Introduction
2.2 Complex Numbers and Harmonic Motion
2.3 Laplace Transformation
2.4 Inverse Laplace Transformation
2.5 Solving Linear Differen
Taking the Ick Factor* Out of Recycled Water
By KATE GALBRAITH
Published: July 25, 2012
http:/www.nytimes.com/2012/07/26/business/global/26iht-green26.html?_r=0
AUSTIN, TEXAS Cleaned-up sewage is
nobodys first choice for drinking water. But
some parts of
YOUR TASK As part of the 214 theme for this semester (Towns and Cities) you have been researching the subject of water shortage in the Kingdom and likely problems associated with this
topic. You have just found your sixth and final source. Your instructor
214 122 Spring 2013 Midterm: suggested answers
APA REFERENCE
HANDWRITTEN with underlining instead of italics
Galbraith, K. (2012, July 25). Taking the 'ick' factor out of recycled water. The New York Times.
Retrieved from http:/www.nytimes.com/2012/07/26/
214 112 Midterm: Suggested answers
CITATION 10%
Nestle, M. (2011, October 22). Obesity's match.New Scientist, 30-31.
SUMMARY 40%
The Danish government has recently taxed unhealthy foods to reduce obesity in the country; however the new
policy is now being
Problem 1:
continuity
A 90 elbow is used to direct water flow at a rate of 25 kg/s in a horizontal pipe upward. The
diameter of the entire elbow is 10 cm. The elbow discharges water into the atmosphere, and thus
the pressure at the exit is the local atmos
Your task: For the past few weeks you have been researching the growing problem of overweight and obesity
and the problems associated with this topic. You have finished your three-level outline (below). You have just
found your sixth and final source. You