1. Example 1: Find the magnitude and phase angle of
Example 2: Find the Laplace Transform of
ME 431, Lecture 2
ME 431, Lecture 2

2. Laplace Transform Table
Impulse t
Step t
Ramp
ME 431, Lecture 2

3. Laplace Transform Theorems
ME 431, Lecture 2
ME 431, Lecture 2

4. Example 4: Find of the system
Example 3: Given Find
Example 4: Find of the system
Given that x = u(t) and all initial conditions
are zeros
ME 431, Lecture 2
ME 431, Lecture 2

5. Example 5: Find the inverse Laplace transform of
ME 431, Lecture 2
ME 431, Lecture 2

6. Partial-Fraction Expansion
If the order of B(s) is less than the order of A(s) and pk (k = 1, 2, …n) are distinct real numbers, then we have
Where
ME 431, Lecture 2
ME 431, Lecture 2

7. A system is represented by the following differential equation:
Problem
A system is represented by the following differential equation:
1. Find the expression of the transfer function for the system, Y(s)/X(s).
2. Represent the transfer function as a block diagram.
3. Find the final value of output, y(∞), when x = δ(t).
ME 431, Lecture 2
ME 431, Lecture 2