Question

laplace transform of f(t)=kt?

Answer 1

assuming k is some number , then we would have to look for laplace transform of the form \[t^{n}f(t)\] then f(t) would be just any constant k right ?

Answer 2

so if f(t) is a function which have Laplce transform F(s) the laplace of the whole thing you can find by applying this formula
\[(-1)^{n}\frac{ d^{n}F(s) }{ ds^{n} }\]

Answer 3

well lap.tr. off k is k/s, know for kt?

Answer 4

yes laplace transform of k is k/s so acording to the formula i wrote above you need to look for first derivative of k/s (since n=1 because t is of degree 1 )

Answer 5

so you would have \[(-1)^{1}\frac{ d }{ ds }(\frac{ k }{ s })=-1(-\frac{ k }{ s^2 })=\frac{ k }{ s^{2} }\]

Answer 6

im not familiar with this formula, I'm using f(t)e^(-st)

Answer 7

oh you need to find it by definition ?

Answer 8

with this formula :\[\int\limits_{0}^{\infty}{e^{-st}f(t)dt}\]

Answer 9

yes

Answer 10

ok so since it is integral with bounds from 0 to infinity we need to rewrite it with limit going to infinity , you familiar with solving this kind of integrals ?

Answer 11

I'm getting lost simplifying

Answer 12

did you try solving the integral ?

Answer 13

you are getting lost simplifying what ?

Answer 14

sorry had to go take a test

Answer 15

its cool dont worry , you needed help not me so ... i hope the test went well xD

Answer 16

i breezed throughout all the questions except the last one (only 5 questions) need an A to pass the test, the laplace transform is an extra credit project which I'm doing to help me hopefully pass

Answer 17

oh well make sure u do that laplace transform its easy ^^