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

 

laplace question 1 and 2 solution

Exercises: Find the Laplace transforms of the following functions by hand and verify results using Matlab. General Laplace transform table F(t) f(t) 1 1/s t^n n!/s^(n+1) e^at/e^(-at) 1/(s-a)/1/(s+a) sin⁡ax a/(s^2+a^2 ) cos⁡ax s/(s^2+a^2 ) y y ̃ y^̕ ̕sy ̕-y(0) y̋ s^2 y ̄-sy(0)-y ̕(0) x(t)=t Hand calculation ɭ[x (t)] =∫_0^∞▒〖x(t)e^(-st) dt〗 = ∫_0^∞▒〖te^(-st) dt〗 Using differentiation by parts Let u=t and dv=e^(-st) du=1 and also v will be v=〖-e〗^(-st)/s x(t)= ∫_0^∞▒〖te^(-st) dt〗=〖-te〗^(-st)/s ǀ_0^∞ +1/s ∫_0^∞▒〖e^(-st)...

• laplace Transform solutions question 1 and 2.docx 21 KB

laplace question 1 and 2 solution

ECET 345 LAB WEEK 2 Last week was a basic... The Laplace transformxxxxxxxxxx functions into f(t) that are defined by whereby: Laoplace transforms the f(t)xxxxxxxxxxx function that can also be obtained with a Matlab’s function Laplace. The...

• ECET 345 LAB WEEK 2 Laplace Transform.docx 93 KB

laplace question 1 and 2 solution

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• ECET 345 LAB WEEK 2 Laplace Transform Solution.docx 3 MB

laplace question 1 and 2 solution

ECET 345 LAB WEEK 2 Last week was a basic... The Laplace transforms functions into f(t) that are defined by whereby: Laoplace transforms the f(t) function that can also be obtained with a Matlab’s function Laplace. The syntax is L=laplace(f)...

• ECET 345 LAB WEEK 2 Laplace Transform.docx 93 KB