Question

find the inverse laplace transform of (3/(2s+5)^3).

Answer 1

hmm

factor out the 2 is my first thought; try to get this into:

1/(s+k)^3

Answer 2

I'm confused on how to do this problem in general. i don't know what Laplace transform is

Answer 3

if you dont know what Laplace transform is, then you reallya re asking the wrong question to begin with .....

Answer 4

the Laplace transform is an integral transform that .. well, transforms a function from an integration to an algebra problem

Answer 5

there is a table of Laplace transforms that we try to get this thing to look like in order to undo it back into what it looked like to begin with

Answer 6

my idea for the inverse is to basically format it into something invertable

Answer 7

\[\frac{3}{(2(s+\frac{5}{2}))^3}\]
\[\frac{3}{8(s+\frac{5}{2})^3}\]
\[\frac{2*\frac{3}{2}}{8(s+\frac{5}{2})^3}\]
\[\frac{3}{16}L\left\{\frac{2}{(s+\frac{5}{2})^3}\right\}\]

Answer 8

i got no idea how right t is tho; so id have to chk my resulte wolfs with th

Answer 9

laptop mistype me up lol

Answer 10

http://www.wolframalpha.com/input/?i=laplace+inverse&f1=3%2F%282x%2B5%29%5E3&f=InverseLaplaceTransformCalculator.transformfunction_3%2F%282x%2B5%29%5E3&f2=x&x=6&y=7&f=InverseLaplaceTransformCalculator.variable1_x&f3=t&f=InverseLaplaceTransformCalculator.variable2_t

i was basically right :)

Answer 11

why do the initial variable x become t?

Answer 12

is it supposed to show that it's not the original problem?

Answer 13

the Laplace transform takes a function of one variable; namely t and transforms it into a function of another variable, namely s ; but i chose x in this place cause the wolf was being nitpicky and wanted to read the s as seconds instead of a variable ....

Answer 14

so after you formed the function to a more workable problem, you just plug into a formula?

Answer 15

the laplace tables tell me:

L{t^n} = n!/s^(n+1)

so if I can get the function you provided into this format, I can undo (or invert) the Laplace transform to get back to the original function

i just wasnt to sure what i should do to the extra +5/2 in the bottom

Answer 16

the site seems buggy tonight ...

Answer 17

what do you mean by the original function?

Answer 18

and how do you get from L (2/(s+5/2)^3) to plug into the form n!/s^(n+1)

Answer 19

where is n?

Answer 20

since the underside has ^3; which matches up to ^(n+1) ; n has to equal 2

Answer 21

2*3/2 = 3 so I just rewrote the top to my advantage

Answer 22

same with the bottom; i factored out a 2 down there

Answer 23

pull the constants out that aint needed and your set to undo it

Answer 24

so can we completely ignore constants?

Answer 25

the Laplace is a linear transform, meaning it has the following properties

L{a+b} = L{a} + L{b}

and for any constant k,

L{ka} = k L{a}

so the constants can be pulled out as concerns the actual operations

Answer 26

oh that makes sense!

Answer 27

as such, we can format these things by using constants to get them to a proper form that can be inverted

Answer 28

thank you!

Answer 29

youre welcome