Question

Diff EQ: Question is in the comments

Answer 1

Find the Laplace transform of f(t = )t*sin(at) using the definition \[\int\limits_{0}^{\infty} f(t)e^{-st}dt\]

Answer 2

f(t) = t*sin(at)

Answer 3

this is a by parts process isnt it? which just tables out

Answer 4

i've gotten to a certain point and then I'm stuck so let me type what ive gotten

Answer 5

use Euler's formula - the imaginary part

made for Laplace Transforms.....

Answer 6

I get two integration by part problems and for the fist one i end up getting \[t* \frac{e^{ia-st}}{ia-s} - \frac{e^{ia-st}}{(ia - s)^2}\] evaluated from 0 to infinity

Answer 7

Its been a while since i've done the infinite integrals so how to procede from here?

Answer 8

the exponent of e should be iat-st

Answer 9

essentially, e^(-inf) = 0 for the upper limit

Answer 10

at t=0, that -1/(ia-s)^2

Answer 11

im not experienced at the euler form so i cant determine if you worked it correctly or not

Answer 12

so for evaluating at infinity i would get: infinity*0 - 0 asuming i worked the problem out correctly?

Answer 13

yes

Answer 14

infinity*0 is indeterminate isn't it?

Answer 15

its 0 for all practical purposes lol

Answer 16

Ohh lol ok

Answer 17

compare t and e^(-t) , e^(-t) moves quicker and farther than t, so it tends to dominate in my mind

Answer 18

e^(-st) goes to zero faster than 't' goes to infinity

Answer 19

i see, thats where i was confused. I thought i had to break out l'whatever's rule

Answer 20

Lhop, yeah :)

Answer 21

Awesome. Thank you!

Answer 22

youre welcome