Question

partials fractions help please...
s^2(s+2)/(s^2-16)

Answer 1

let me guess, for inverse laplace transform ?

Answer 2

factor s^2-16 first

Answer 3

lol yeah

Answer 4

a^2-b^2 = (a+b)(a-b)

Answer 5

so s^3(s+2)/(s^2+4)(s^2-4)

Answer 6

is it s^4 -16 ? O.o

Answer 7

yeah sorry

Answer 8

ok, no problem :)

Answer 9

for denominator of \(s^2 \pm a^2\) or any other quadratic,
we use
\(\Large \dfrac{As+B}{quadratic}\)

Answer 10

so,
\(\dfrac{s^2(s+2)}{()()}= \dfrac{As+B}{()} +\dfrac{Cx+D}{()}\)
i feel lazy to fill denominators
hope you can fill it :P

Answer 11

yeah so far so good followoing along on paper

Answer 12

(as+d)(s^2-4) + (bx+c)(s^2+4) = s^3 = 2s^2

Answer 13

I mean = s^3 + 2s^2

Answer 14

expand left side
so that you can compare the co-efficients

Answer 15

as^3 + bs^3 = 1 and as^2 + cs^2 =2

Answer 16

you mean as^3+bs^3 = s^3
giving a+b = 1
?

Answer 17

yes I have a+b = 1

Answer 18

start with easier terms
-4d+4c = 0
d=c

Answer 19

and a = b from -4a +4b = 0

Answer 20

got that

Answer 21

@hartnn

Answer 22

but the question has s^4 -16
read comments please

Answer 23

@Hanishala I typed in wrong term to start with );

Answer 24

ok so I also have ds^2 + cs^2 = 2s^2 correct??

Answer 25

sorry i didnot see it

Answer 26

its ok

Answer 27

(as+d)(s^2-4) + (bs+c)(s^2+4) = s^3 + 2s^2

d+c =2
yes correct
o on

Answer 28

*go on

Answer 29

so we have d - 1, c =1, a =1/2, b = 1/2 right?

Answer 30

d= 1, c = 1, a =1/2 b = 1/2

Answer 31

correct?

Answer 32

let me cross check again

Answer 33

we made an error from the beginning :(

Answer 34

where at?

Answer 35

sorry

s^2-4
can be factored further

Answer 36

ok

Answer 37

which means s+2 gets cancelled!

Answer 38

ahh

Answer 39

you can make s^2 -4 = (s-2) +(s+2 )
and continue

Answer 40

s^3/ (s^2+4)(s-2) = A/(s-2) + (Bs+C)/(s^2+4)

Answer 41

s^3 = A(s^2+4) + (Bs+C)(s-2)

this is even easier! :)

Answer 42

to find A, plug in s=2 :)

Answer 43

wouldnt it be s^2 on left side now?

Answer 44

yes, sorry typo

Answer 45

but i think you can find A,B,C
try ?

Answer 46

Yeah let me try (;

Answer 47

Thank you both.

Answer 48

so what values did u get ?