Laplace Transform Review
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Transcript of Laplace Transform Review
Laplace Transform Review
A system represented by a differential equation is difficult to model as a block diagram.
Laplace transforms can be used to represent the input , output and system as separate entities.
Also, Laplace transforms makes the inter-relationship of the system’s input and output algebraic.
Sample Problems
1. Find the Laplace transform of
2. Derive the Laplace Transform of the
following time functions
u(t)
tu(t)
sin(wt) u(t)
cos(wt) u(t)
3. Using the Laplace transform pair and the Laplace transform theorems, derive the Laplace transform for the following time functions:
a.
b.
c.
4. Find the Inverse Laplace transform of
INVERSE LAPLACE TRANSFORM
PARTIAL FRACTION EXPANSION
Case 1: Roots of the Denominator of F(s) are real and distinct
Case 2: Roots of the Denominator of F(s) are real and repeated
Case 3: Roots of the Denominator of F(s) are complex or Imaginary
Laplace Transform solution of a
Differential Equation
Examples:
Find the solution of the differential
equation using Laplace Transforms:
assume zero initial conditions