Marie's copy of Find the Laplace transfrom of ode

Error

There was an error loading the page.

Contributors

History

○

Marie Nicholson 6 years, 3 months ago

Created this as a copy of Year 3 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

There are 6 other versions that do you not have access to.

Question statement

Find the Laplace transform of the following differential equation and express it $Q(s)$ as a single fraction:

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

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	4
b	integer	21
c	integer	12
d	integer	7
f	integer	2
g	integer	9

Automatically regenerate variables?

Name

Data type

Value

A random number between and (inclusive) with step size

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `integer`

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap Mathematical expression
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

$Q(s)=$ Unnamed gap

Advice

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

$s^2Q(s)-sq(0)-q'(0)+\var{a}(s(Q(s)-q(0))+\var{b}Q(s)=\frac{\var{c}}{s+\var{d}}$

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

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

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

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

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet

This question is not used in any exams.

Loading...

Error

Marie's copy of Find the Laplace transfrom of ode

Metadata

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

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Loading...

Error

Marie's copy of Find the Laplace transfrom of ode

Metadata

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

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`