### ECET 345 LAB WEEK 2 Laplace Transform

**ECET 345 LAB WEEK 2 Laplace Transform**

**ECET 345**

**LAB WEEK 2**

Last week was a basic introduction to Matlab. This week you will learn how to use three built-in functions (laplace, ilaplace and dsolve).

**Using the syms function**

An expression can be represented using symbols with the syms function.

Let’s study the following example:

syms x y % Declare two symbolic variables x and y

y = x^2 %Declare a function

z=diff(y) %Will calculate the derivative of y and store the value in z.

** **

**How to find the Laplace transform for an expression? **

**Example:** Find the Laplace transform of sin(2t). From the table of Laplace transforms, the Laplace transform of sin(2t) is . Let us do the same calculation in Matlab.

syms t % Declare a symbolic variable t

F=laplace(sin(2*t)) %Calculate Laplace transform, store in F

pretty(F) % print the output in a more readable form

** **

**How to find the inverse Laplace transform for an expression? **

**Example:** Find the inverse Laplace transform of From the previous example, the inverse Laplace transform is sin(2t). The following code will verify this calculation in Matlab.

syms s % Declare a symbolic variable s (the Laplace variable)

f=ilaplace(2/(s^2+4)) %Calculate inverse Laplace transform, store in F

pretty(f) % print the output in a more readable form

** **

**How to solve a differential equation in Matlab? **

**Example: Solve the differential equation ****, with initial conditions x(0)=1 and x’(0)= 0. **

Matlab command:

dsolve('D2x+2*x=0', 'x(0) = 1, Dx(0) = 0')

**Exercises:**

1. Find the Laplace transforms of the following functions by hand and verify results using Matlab.

*1. *

*2. *

*3. *

2. Find the inverse Laplace transform of the following functions by hand and verify results using Matlab.

** **

**1. **

**2. ****F(s)=**

3. Solve the following differential equations by hand and verify results using Matlab.

with x(0) = 1, x' (0) = 0

with x(0) = 1, x' (0) = 0

** **

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