Laplace transform problem

I am stuck on a laplace transform problem, I do not know how to get to the partial decomposition stage.

I have attached the question and my working with it. Please help, revising for my exam.

Thanks a lot.

Reply 1

mqb2766

Attachment?

Original post by mrambitious

Reply 2

mrambitious

Original post by mqb2766

Attachment?

It's not letting me upload it :/

Reply 3

mqb2766

Put it on an image site and link?

Original post by mrambitious

It's not letting me upload it :/

Reply 4

mrambitious

Thanks. Here you go:

https://ibb.co/NC1X8Df

Original post by mqb2766

Put it on an image site and link?

Reply 5

mqb2766

Is it xdotdot or just xdot = 2x-y?
Also remember when you take laplace of a derivative, you multiply by s. This term is missing them appears a few lines down.

Original post by mrambitious

Thanks. Here you go:

https://ibb.co/NC1X8Df

(edited 4 years ago)

Reply 6

mrambitious

Original post by mqb2766

Is it xdotdot or just xdot = 2x-y?

It's just x dot= 2x-y

Reply 7

DFranklin

You need to treat as simultaneous equations in x and y (and solve them to get expressions for x,y in terms of s).

Reply 8

mqb2766

Yup, on the last couple of lines you have two equations in x(s) and y(s). Combine them to get equations in just x and y, then solve.

Edit also
* 1-y(s) for the first equation
* the brackets round s go wrong at the end. Not y(s+1)
* y(s)(s+2), not minus for the second equation.

Original post by DFranklin

You need to treat as simultaneous equations in x and y (and solve them to get expressions for x,y in terms of s).

(edited 4 years ago)

Reply 9

mrambitious

Thanks a lot for your help. I think it's the combining of the equations which I am finding tricky, could you help me here please?

Original post by mqb2766

(edited 4 years ago)

Reply 10

mqb2766

Tbh you've largely done it. Can you repost the working with the mistakes corrected, then i'll help you finish.

Original post by mrambitious

Thanks a lot for your hep. I think it's the combining of the equations which I am finding tricky, could you help me here please?

Reply 11

mrambitious

Original post by mqb2766

Tbh you've largely done it. Can you repost the working with the mistakes corrected, then i'll help you finish.

Okay, here you go

https://ibb.co/NC1X8Df

Reply 12

mqb2766

Same file, no corrections?

Original post by mrambitious

Okay, here you go

https://ibb.co/NC1X8Df

Reply 13

mrambitious

Ah sorry, that was a mistake.

The correct file is :

https://ibb.co/Kz2XXfb

Original post by mqb2766

Same file, no corrections?

Reply 14

mqb2766

That looks better. You've still forgotten to write
sX(s) when you take Laplace of xdot ,but it appears on the next line, so the working is correct, but not sure whether you fully understand. Same for ydot and sY(s).

To combine at the end, simply note that the first equation is
X(s) = 1/(s-2) - Y(s)*(1/(s-2))
Then use the 2nd equation to replace Y(s) and simplify, keeping in factorized form.

Edit, it would probably be easier to combine the expressions before writing as rational polynomials.
Multiply through the X(s)(s-2) equation by (s+2), then substitute for Y(s)(s+2) using the second equation. Then write as rational polynomials.

Original post by mrambitious

Ah sorry, that was a mistake.

The correct file is :

https://ibb.co/Kz2XXfb

(edited 4 years ago)

Reply 15

mrambitious

Original post by mqb2766

I got -5x (s)/(s+2)(s-2)
For the first equation, does this look correct?

I then do the same for the second equation?

Reply 16

mqb2766

Nearly, you should get when you sub
X(s)(s-2)(s+2) = (s+2) - (5X(s)+1)
Which gives
X(s) = (s+1)/(s^2+1)
Do you agree? If not, post your working?

Original post by mrambitious

I got -5x (s)/(s+2)(s-2)
For the first equation, does this look correct?

I then do the same for the second equation?

Reply 17

mrambitious

I am understanding your method now, but could you please explain what happens to the 5x in the equation, it doesn't seem to be accounted for?

Original post by mqb2766

Nearly, you should get when you sub
X(s)(s-2)(s+2) = (s+2) - (5X(s)+1)
Which gives
X(s) = (s+1)/(s^2+1)
Do you agree? If not, post your working?

Reply 18

mqb2766

You put the X(s) terms on the left hand side and combine. Keep the s terms on the right.
Then form the rational polynomial.

Original post by mrambitious

I am understanding your method now, but could you please explain what happens to the 5x in the equation, it doesn't seem to be accounted for?

Reply 19

DFranklin

Original post by mrambitious

I am understanding your method now, but could you please explain what happens to the 5x in the equation, it doesn't seem to be accounted for?

You have (s-2)(s+2) (times x(s)) on the LHS, and -5 x(s) on the RHS. Add 5 x(s) to both sides and you get s^2+1.

At the end of the day, this is basic algebra.

Hard truth: The number of mistakes you're making and the general inability to progress shows that you have a big shortcoming in this area. Applied mathematics questions often require a lot of algebraic manipulation and you are setting yourself up to fail if you can't do that manipulation reliably.