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- From Mathematics, Statistics
- Due on 26 May, 2015 07:44:00
- Asked On 20 May, 2015 09:16:06
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**Linda77****Rating :**0**Grade :****No Rating****Questions :**2**Solutions :**0**Blog :**0**Earned :**$0.00

**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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- Submitted On 21 May, 2015 01:50:21

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**Dr.mandal****Rating :**0**Grade :****No Rating****Questions :**0**Solutions :**10**Blog :**0**Earned :**$104.00

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)
sinax a/(s^2+a^2 )
cosax 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)...

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- Submitted On 25 May, 2015 11:14:13

Solution posted by

**NUMBER1TUTOR****Rating :**87**Grade :****A+****Questions :**0**Solutions :**5075**Blog :**3**Earned :**$14052.07

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...

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- Submitted On 28 May, 2015 11:43:55

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This Tutorial is rated A+ p...

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- Submitted On 06 Jul, 2015 05:58:59

Solution posted by

**NUMBER1TUTOR****Rating :**87**Grade :****A+****Questions :**0**Solutions :**5075**Blog :**3**Earned :**$14052.07

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)...

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