Find the Laplace transform of ode

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Marie Nicholson 6 years, 3 months ago

Created this as a copy of Find the Laplace transfrom of ode.

Name	Status	Author	Last Modified
Year 3 Find the Laplace transfrom of ode	Ready to use	Frank Doheny	06/03/2018 13:31
Find the Laplace transfrom of ode	Ready to use	Frank Doheny	26/02/2018 07:39
Find the Laplace transform of ode	draft	Marie Nicholson	23/11/2018 13:23
Marie's copy of Find the Laplace transfrom of ode	draft	Marie Nicholson	22/11/2018 09:50
Laplace: Find the Laplace transfrom of ode	draft	Clare Lundon	05/02/2019 08:17
Laplace: Find the Laplace transform of ode	draft	Clare Lundon	09/02/2019 19:49
Priyanka's copy of Laplace: Find the Laplace transform of ode	draft	Priyanka Pandya	12/02/2020 06:53
Ugur's copy of Laplace: Find the Laplace transform of ode	Ready to use	Ugur Efem	01/03/2023 09:20
Ugur's copy of Year 3 Find the Laplace transfrom of ode	Ready to use	Ugur Efem	20/02/2023 14:18

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Question statement

Find the Laplace transform of the following differential equation and express it as a single fraction:

$\frac{d^2x}{dt^2}+\var{a}\frac{dx}{dt}+\var{b}x(t)=\var{c}e^{-\var{d}t}$ where $x(0)=\var{f}$ and $x'(0)=\var{g}$

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			Name	Type	Generated Value

a	integer	6
b	integer	12
c	integer	8
d	integer	7
f	integer	6
g	integer	3

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1. Gap Mathematical expression
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$X(s)=$ Unnamed gap

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$\frac{d^2x}{dt^2}+\var{a}\frac{dx}{dt}+\var{b}x(t)=\var{c}e^{-\var{d}t}$ where $x(0)=\var{f}$ and $x'(0)=\var{g}$

$s^2X(s)-sx(0)-x'(0)+\var{a}(s(X(s)-x(0))+\var{b}X(s)=\frac{\var{c}}{s+\var{d}}$

$s^2X(s)-\var{f}s-\var{g}+\var{a}sX(s)-\var{a}*\var{f}+\var{b}X(s)=\frac{\var{c}}{s+\var{d}}$

$s^2X(s)+\var{a}sX(s)+\var{b}X(s)=\frac{\var{c}}{s+\var{d}}+\var{f}s+\simplify{{g}+{a}*{f}}$

$(s^2+\var{a}s+\var{b})X(s)=\frac{\var{c}+(\var{f}s+\simplify{{g}+{a}*{f}})(s+\var{d})}{s+\var{d}}$

$X(s)=\frac{\simplify{{f}s^2+({a}*{f}+{g}+{d}*{f})s+(({g}+{f}*{a})*{d}+{c})}}{(s+\var{d})(s^2+\var{a}s+\var{b})}$

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This question is used in the following exams:

LT1: lntroduction to Laplace Transforms by Marie Nicholson in MATH6059.
lntroduction to Laplace Transforms by Violeta CIT in Laplace Transforms.
Laplace Transforms by Julie Crowley in Julie's workspace.

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Marie Nicholson 6 years, 3 months ago

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Generated value: `integer`

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Find the Laplace transform of ode

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Marie Nicholson 6 years, 3 months ago

Error in variable testing condition

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Generated value: integer

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Gap-fill

Generated value: `integer`