Question

can someone confirm my working please? it's kinda hard stuff...

Answer 1

what work ill see if i can help

Answer 2

laplace transform of f(t) = 5ut + 5e^(-5t) ut + sin (wt) u(t)

Answer 3

have F(s) = 5/s + 5/(s+5) + w/(s^2 + w^2)

is this correct?

Answer 4

@mathmale ?

Answer 5

apologies, should be:
f(t) = 5u(t) + 5e^(-5t) u(t) + sin (wt) u(t)

Answer 6

Yes, that's a lot better. I was going to ask you to re-write those unit step functions.
You can use the table you shared with another student a few minutes ago to find the Laplace Transforms of each of the three individual terms of your f(t).
Yes, the L. transform of 5u(t) is 5/s.

Look at the table. What is the L. t of e^t * u(t)?

Answer 7

1/ s+a

Answer 8

L {e^-at * u(t) } = 1/ s+a

Answer 9

i cant elp with that sorry

Answer 10

Then what is the L. transform of e^(-5t) u(t)?

Answer 11

5/(s+5)... no?

Answer 12

Before I answer that, what happens to the " 5 " in front of e^(-5t) in your original expression?

Answer 13

it's removed from the transform, then brought back in at the end.
so the transform i think goes from 1/(s+a) whis is 1/(s+5) to become 5/s+5... yeah?

Answer 14

Basically, yes. Given 5e^(-5t), separate the coefficient 5 from this expression, find the L. t. of the function e^(-5t), and then multiply the resulting L. t. by that coefficient 5. This is the "constant coefficient rule."

Answer 15

Now, what's the L. t. of sin (omega*t)?

Answer 16

w/S SQRD + W SQRD?

Answer 17

sorry, caps
omega/(s^2 + omega ^2) ?

Answer 18

Looks like you're right on target.
To re-cap: Find the L. t. of each term in your original expression separately. Then add together all the L. transforms.

Answer 19

ok... but at the end, not that its transformed... do i multiply it out so it has common denominator and i can add the numerators... or is that wrong?

Answer 20

also, cheers for the dbl check @mathmale

Answer 21

My pleasure! See you again on OpenStudy.