Inverse Laplace transform: irreducible quadratic factor

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Frank Doheny

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Frank Doheny

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7 years, 2 months ago

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Frank Doheny 7 years, 1 month ago

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Frank Doheny 7 years, 2 months ago

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Created this as a copy of Inverse Laplace transform: irreducible quadratic factor.

Name	Status	Author	Last Modified
Inverse Laplace transform: irreducible quadratic factor	draft	Frank Doheny	06/03/2018 13:33
Inverse Laplace transform: irreducible quadratic factor	Ready to use	Frank Doheny	26/02/2018 07:36
Marie's copy of Inverse Laplace transform: irreducible quadratic factor	draft	Marie Nicholson	22/11/2018 09:45
Laplace transform: irreducible quadratic factor	draft	Marie Nicholson	23/11/2018 13:23
Laplace: Inverse Laplace Completing the Square	draft	Clare Lundon	08/04/2020 21:13
Ugur's copy of Laplace: Inverse Laplace Completing the Square	Ready to use	Ugur Efem	20/02/2023 14:22
Ugur's copy of Laplace transform: irreducible quadratic factor	Ready to use	Ugur Efem	20/02/2023 14:36

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Question statement

Having found the partial fraction breakdown:

$X(s)=\frac{\var{A}}{s+\var{a1}}+\frac{\var{B}s+\var{C}}{s^2+\simplify{{b1}*2}s+\var{c1}}$

Give any introductory information the student needs.

			Name	Type	Generated Value

A	integer	9
a1	integer	2
B	integer	5
b1	integer	12
C	integer	11
c1	number	160
f	integer	4

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Generated value: `integer`

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1. Gap Mathematical expression
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Write down the inverse Laplace transform

$x(t)=$ Unnamed gap

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$X(s)=\frac{\var{A}}{s+\var{a1}}+\frac{\var{B}s+\var{C}}{s^2+\simplify{{b1}*2}s+\var{c1}}$

$X(s)=\frac{\var{A}}{s+\var{a1}}+\frac{\var{B}s+\var{C}}{(s+\var{b1})^2+\simplify{{c1}-{b1}^2}}$

$X(s)=\frac{\var{A}}{s+\var{a1}}+\frac{\var{B}(s+\var{b1})-\simplify{{B}*{b1}-{C}}}{(s+\var{b1})^2+\simplify{{c1}-{b1}^2}}$

$x(t)=\var{A}e^{\var{a1}t}+\var{B}e^{-\var{b1}t}cos\left(\sqrt{\simplify{{c1}-{b1}^2}}t\right)+\frac{-\simplify{{B}*{b1}-{C}}}{\sqrt{\simplify{{c1}-{b1}^2}}}e^{-\var{b1}t}sin\left(\sqrt{\simplify{{c1}-{b1}^2}}t\right)$

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Inverse Laplace transform: irreducible quadratic factor

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Frank Doheny 7 years, 1 month ago

Frank Doheny 7 years, 2 months ago

Frank Doheny 7 years, 4 months ago

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Generated value: `integer`

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Inverse Laplace transform: irreducible quadratic factor

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Frank Doheny 7 years, 1 month ago

Frank Doheny 7 years, 2 months ago

Frank Doheny 7 years, 4 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`