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1answer
43 views

Laplace Transform assistance

Find the inverse laplace transform of: $\frac{25}{(s-1)^2(s^2+4)}$ $\frac{25}{(s-1)^2(s^2+4)}=\frac{A}{s-1}+\frac{B}{(s-1)^2}+\frac{C}{s^2 + 4}$ $$25=A(s^2+4)(s-1)+B(s^2+4)+C(s-1)^2$$ ...
2
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1answer
39 views

help in Laplace and partial fractions

Can any one teach me how to solve C2.(a) and (b) step by step? C2. (a) Resolve $\frac{1}{s^2(s^2+s+1)}$ into partial fractions of the form $\frac{A}{s}+\frac{B}{s^2}+\frac{Cs+D}{s^2+s+1}$. Hence, ...
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0answers
19 views

Using partial fraction for inverse Laplace transform of $1/[s(s+5)^2]$

my question is the last part $1/5(s+5)^2$, how is it become $-5te^{-5t}$ I thought is should be -$1/5 te^{-5t}$
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1answer
33 views

Inverse Laplace transform (using table) when denominator cannot be factored

Usually when performing inverse Laplace transforms, I decompose the function into partial fractions, and then look up standard transforms in a table. For example: $$Y(s) = ...
0
votes
1answer
37 views

Using Laplace transforms to solve a convolution of two functions

Hi I have this problem where I need to take the convolution of functions and I am not sure if I got the right answer or something close so any advice or help would be very appreciated. So here is the ...
1
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0answers
29 views

Laplace transform of Differential Equation with a piecewise function

Hi I have this question and I am horribly stuck at one part and I cant seem to figure out if i did something wrong so any advice or help would be greatly apprecaited. Here is the question: ...
1
vote
2answers
23 views

Converting to a partial fraction.

I'm trying to do an inverse Laplace operation on $I(s)$ shown below but I'm struggling on finding what $A$ & $C$ are on the partial fraction and how to do it. I calculated what $B$ equals by ...
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1answer
46 views

Laplace transform of initial value problem, stuck on partial fractions.

The problem im given is: Use Laplace transforms to solve the initial value problem. $$\ddot x +x=\sin(2t)$$ $$x(0)=0=\dot x(0)$$ I first do the following Laplace transforms: $$\mathcal{L}\{\ ...
0
votes
1answer
70 views

inverse laplace using partial fractions and completing square

what is the inverse Laplace transform of this equation $$\frac{1}{(s+1)(s^2+s+1)}$$ I know that completing the square for the quadratic term is required to avoid complex roots and then I need to use ...
1
vote
2answers
188 views

Solve second order differential equation with Heaviside function using Laplace transform

The equation is: $$y'' + 3y = u_4(t)\cos(5(t-4)), \quad y(0) = 0, \quad y'(0) = -2$$ Here $u_4$ is the Heaviside function with activation switch at $t=4$. I can get all the way to the partial ...
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2answers
88 views

Laplace question continued (partial fractions)

Last night I attempted and successfully finished (with the help of stackexchange) the first part to this question on laplace transformations: Laplace question - help needed The second part to this ...
3
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1answer
53 views

How do I apply partial fraction expansion on $\dfrac{K}{(a+bz^{-1})(x+yz)}$?

I want to apply partial fraction expansion on $\dfrac{K}{(a+bz^{-1})(x+yz)}$. I'm not able to do it in the standard way, because one term has $z^{-1}$ term and the other has $z$. What is the approach ...
2
votes
1answer
101 views

Basic Partial Fractions

I feel super foolish asking this, but I've reached a mental block. I'm trying to find the inverse laplace transform of: $$\frac{s+3}{(s + 1)^2 (s-2)}$$ but, when I expand it into partial ...
2
votes
1answer
52 views

Help with partial fraction decomposition

So I was working on problem 16 in Elementary Differential Equations 9th edition by DiPrima and I get to the point where I'm using partial fraction's to separate : $\displaystyle {1 \over ...
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1answer
89 views

Laplace inverse of $\frac{e^{-s}(3s^2-s+2)}{(s-1)(s^2+1)}$

I thought maybe you could fist solve $\frac{(3s^2-s+2)}{(s-1)(s^2+1)}$ using partial fractions and later solve the $e^{-s}$ separately as it is a $d(t-1)$ (Dirac delta function). As you solve the ...
3
votes
1answer
115 views

Help with a partial fraction decomposition

One of my homework problems last week was to find the inverse Laplace transform of the following: $$F(s)=\frac{2s+1}{s^2-2s+2}.$$ The answer is $f(t)= 2e^t \cos t + 3e^t \sin t$. Obviously once ...
0
votes
2answers
108 views

Partial fraction with same denominator

Is the following fraction (actually a Laplace transform) a kind of partial fraction? $$\frac{4s+3}{{s^2}+3}$$ Can this be solved this way? $$\frac{A}{s}+\frac{B}{s+{\frac{3}{s}}}$$ If not can you ...
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3answers
1k views

Inverse Laplace transform with partial fraction

I have the transform below: $$\frac{(7s+2)(2s-5)}{{s^2}(s-2)}$$ I think this is should be partial fraction to be solved. Can you please help me figure how to consider A, B, C and denominators?
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1answer
227 views

Using z-transforms to solve difference equations.

I am faced with the following question and would appreciate any help you may be able to offer: It is not homework, I know the first and second shift theorems and based on the other examples I have ...