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Sheet No. 1 (2017-2018) : Q1) Solve The Following Using Laplace Transforms

This document contains 4 questions regarding Laplace transforms and their inversions. Question 1 asks to solve 3 differential equations using Laplace transforms. Question 2 asks to invert 3 given Laplace transforms. Question 3 asks to find and graph the forcing function for 2 given Laplace transforms. Question 4 asks to determine the value of a given function f(t) at t = 1.5 and t = 3. The document provides an assignment sheet from Soran University's Chemical Engineering department regarding process control.

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عبداللە عمر ابراهیم
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56 views1 page

Sheet No. 1 (2017-2018) : Q1) Solve The Following Using Laplace Transforms

This document contains 4 questions regarding Laplace transforms and their inversions. Question 1 asks to solve 3 differential equations using Laplace transforms. Question 2 asks to invert 3 given Laplace transforms. Question 3 asks to find and graph the forcing function for 2 given Laplace transforms. Question 4 asks to determine the value of a given function f(t) at t = 1.5 and t = 3. The document provides an assignment sheet from Soran University's Chemical Engineering department regarding process control.

Uploaded by

عبداللە عمر ابراهیم
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© © All Rights Reserved
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Sheet No.

1
(2017-2018)
Soran University Fourth Class
College of Engineering Process Control
Chemical Engineering Department Dr. ARKAN JASIM HADI

Q1) Solve the following using Laplace transforms:

d 2 x dx
a)   x  1 If x(0)  x ' (0)  0
dt 2 dt
d 2x dx
b) 2  2  x  1 If x(0)  x ' (0)  0
dt dt
2
d x dx
c) 2  3  x  1 If x(0)  x ' (0)  0
dt dt

Q2) Invert the following transforms:

3s
 
a)
s  1 ( s 2  4)
2

1
b)
s ( s  2s  5)
2

3s 3  s 2  3s  2
c)
s 2 ( s  1) 2

Q3) Find and graph the forcing function f(t) for the following Laplace transforms:

1 e  s  e 2 s e 3s
a)  
s s2 s
s 2 s
1  2e  e
b)
s2

Q4) Determine f(t) at t = 1.5 and at t = 3 for following function:

f (t )  0.5u (t )  0.5u (t  1)  (t  3)u (t  2)

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