Turn on thread page Beta
 You are Here: Home >< Maths

urgent laplace transform question! watch

1. hey dudes long time no speak,
matter of urgency for uni work 2moro - any help greatly appreciated.
1. whats the laplace of
(e^(-pie s)) / s^2 + 4
its to do with the heaviside function...

2. whats the laplace of f(t) = [H(t - 1) - H(t - 2)]t ?

3. find x(t) when : (s - 2) x(t) - s y(t) = -0.5
and s x(t) + (s - 2) y(t) = (4 + 3s^2) / 2s^s
(differential equations)

as i said any help is definitely needed
thanks
x o x
2. You sure you dont want the inverse for 1)?
3. (Original post by JamesF)
You sure you dont want the inverse for 1)?
probably! i need anything, im a big ball of confusion! do u think u can help me?

x o x
4. Possibly ...gimme a few minutes
5. (Original post by JamesF)
Possibly ...gimme a few minutes
aww thanks!! good luck!!
x o x
6. Right, i'll have a go...
Do you know the result:
e^-(cs).f(s) = L{ H(t-c).F(t-c) } ??

Taking c = pi, and f(s) = 1/(s^2 + 4), you get the answer for the first question.
7. 2) L{ H(t-c) } = integral from 0 to infinity of e^(-st).H(t-c) dt

But H(t-c) is 0 until t > c, so you can just change the limits from 0 to c, and get rid of the heavyside function, leaving
integral from c to infinity of e^(-st) dt = 1/s * e^(-cs)

So the transform of f(t) = H(t-1) + H(t-2) is just e^(-s) + 0.5e^(-2s)

Then L{ t.f(t) } = -f '(s), so the answer to the second question is e^(-s) + e^(-2s)

I think
8. For the third, i think you just eliminate x(t) to find y(t) and then go back, eliminate y(t) to find x(t).
Im not sure what x(t) and y(t) are (possibly x(t) = L{x} ? would make sense), so i dont know how the differential equations come in.

Turn on thread page Beta
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: November 9, 2004
Today on TSR

Find your uni chat thread

Get ahead with your application

University open days

• University of East Anglia (UEA)
Could you inspire the next generation? Find out more about becoming a Secondary teacher with UEA… Postgraduate
Thu, 18 Oct '18
• University of Warwick
Undergraduate Open Days Undergraduate
Sat, 20 Oct '18
• University of Sheffield
Undergraduate Open Days Undergraduate
Sat, 20 Oct '18
Poll
Useful resources

Make your revision easier

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

How to use LaTex

Writing equations the easy way

Study habits of A* students

Top tips from students who have already aced their exams

Create your own Study Planner

Never miss a deadline again

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.