Ugur's copy of Laplace transform #2 - Trig functions

Error

There was an error loading the page.

Contributors

Feedback

From users who are members of Ugur's workspace :

Ugur Efem

said

Ready to use

2 years, 1 month ago

History

○

Ugur Efem 2 years, 1 month ago

Published this.

○

Ugur Efem 2 years, 1 month ago

Gave some feedback: Ready to use

○

Ugur Efem 2 years, 2 months ago

Created this as a copy of Laplace transform #2 - Trig functions.

Name	Status	Author	Last Modified
Find the Laplace transform	Ready to use	Frank Doheny	26/02/2018 07:42
Find the Laplace transform #2	Ready to use	Frank Doheny	26/02/2018 07:40
Find the Laplace transform #3	Ready to use	Frank Doheny	26/02/2018 07:40
Find the Laplace transform	draft	Marie Nicholson	23/11/2018 13:20
Find the Laplace transform #2	draft	Marie Nicholson	23/11/2018 13:20
Find the Laplace transform #3	draft	Marie Nicholson	23/11/2018 13:19
Laplace transform #1 - powers of t and exp	draft	Marie Nicholson	26/06/2019 15:55
Laplace transform #2 - Trig functions	draft	Marie Nicholson	23/11/2018 13:39
Laplace transform #3 - powers of t by exp	draft	Marie Nicholson	23/11/2018 13:41
Priyanka's copy of Laplace transform #1 - powers of t and exp	Ready to use	Priyanka Pandya	10/02/2020 16:12
Ugur's copy of Laplace transform #1 - powers of t and exp	Ready to use	Ugur Efem	20/02/2023 14:12
Ugur's copy of Laplace transform #3 - powers of t by exp	Ready to use	Ugur Efem	20/02/2023 14:11
Ugur's copy of Laplace transform #2 - Trig functions	Ready to use	Ugur Efem	20/02/2023 14:15

There are 15 other versions that do you not have access to.

Question statement

What is the Laplace transform for the function:

$x(t)=\var{a}\sin({\var{n}t})+\var{b}\cos({\var{k}t}).$

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	2
b	integer	6
k	integer	7
n	integer	2

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`

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.

$X(s)=$ Unnamed gap

Advice

By the linearity of Laplace Transform:

$X(s)=\mathcal L\{\var{a}\sin({\var{n}t})+\var{b}\cos({\var{k}t})\} = \var{a}\mathcal L\{\sin({\var{n}t})\}+\var{b}\mathcal L\{\cos({\var{k}t})\}.$

From Laplace Transform table one can read

$\mathcal L\{\sin({\var{n}t})\} = \frac{\var{n}}{s^2 + \var{n}^2} \quad \mbox{ and } \quad \mathcal L\{\cos({\var{n}t})\} = \frac{s}{s^2 + \var{k}^2}.$

Hence

$X(s)=\mathcal L\{\var{a}\sin({\var{n}t})+\var{b}\cos({\var{k}t})\} = \var{a}\mathcal L\{\sin({\var{n}t})\}+\var{b}\mathcal L\{\cos({\var{k}t})\} = \frac{\simplify{{a}*{n}}}{s^2 + \simplify{{n}^2}} + \frac{\var{b}s}{s^2 + \simplify{{k}^2}}.$

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 used in the following exam:

Laplace Transforms by Ugur Efem in Ugur's workspace.

Loading...

Error

Ugur's copy of Laplace transform #2 - Trig functions

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Ugur Efem 2 years, 1 month ago

Ugur Efem 2 years, 1 month ago

Ugur Efem 2 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Loading...

Error

Ugur's copy of Laplace transform #2 - Trig functions

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Ugur Efem 2 years, 1 month ago

Ugur Efem 2 years, 1 month ago

Ugur Efem 2 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`