laplace transformation
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how to do ar?
i mean, i got dat subsidiary equation, but i dunnoe how to further manipulate it by using partial fraction.
anyone can shed some light into it? -
(As+B)/(s^2+4) + (Cs+D)/(S^2+2) = 2/(s^2+4)(s^2+2)
Solve for A , B, C, D and will be factorised -
hmm. still dun understand.....nvm....
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Dont understand ,hah???
Coz, yr question answer wrong mah....
lol... if u work backwards, u cant even get back to the question
if u work using homengous equation, u also can get the answer...
1)
Laplace the answer :
1/4* [ 1/(S+2) + (s-2)/(s^2 + 4) ]
= 1/4 (8/(s+2)(s^2+4)
= 2/(s+2)(s^2+4)
!= question
2) Homengous equation :
Steady state respone :
y(t) = 0
Transient respone :
y^2 + 2 = 0
y = +/- j2
General solution for y should be Acoswt + Bsinwt
Not too sure on part 2...
But if u work backward laplace, the answer is wrong lah... -
oo....blur liao. working on laplace for the past 4 hrs.....hmm...nvm i check again~Originally posted by ispyyy:Dont understand ,hah???
Coz, yr question answer wrong mah....
lol... if u work backwards, u cant even get back to the question
if u work using homengous equation, u also can get the answer...
1)
Laplace the answer :
1/4* [ 1/(S+2) + (s-2)/(s^2 + 4) ]
= 1/4 (8/(s+2)(s^2+4)
= 2/(s+2)(s^2+4)
!= question
2) Homengous equation :
Steady state respone :
y(t) = 0
Transient respone :
y^2 + 2 = 0
y = +/- j2
General solution for y should be Acoswt + Bsinwt
Not too sure on part 2...
But if u work backward laplace, the answer is wrong lah... -
another question:
my qns is the one dat i hav circled.... v confusing now.... -
inverse laplace {3/(s^2+9)^2}
= inverse laplace{(3/s)(g(s)} ---->where g(s) = 1/(s^2+9)
= 3intregal {g(t)} --->given inverse laplace of (1/s)g(s) = intergal of g(s)
= 1/3cos3t ---->where g(t) = 1/3sin3t
Wa... yr paper so difficult 1 ,hah???
I really have to refer alot leh... to remember :p -
Dont blur...
laplace transform just apply fomular only....
Probably, the difficult part is factorising ....
Just follow the examples as below lor :
1/(s)(s+1) = A/s + B/(s+1) Find A and B
1/(s)(s+1)^2 = A/s + B/(s+1) + C/(s+1)^2 Find A, B and C
1/(s)(s^2+1) = A/s + (Bs+C)/(s^2+1) Find A,B and C
1/(s)(s^3+1) = A/s +(Bs^2 + Cs + D)/(s^3+1) Find A,B,C and D
Just remember the numerator must contain expression of order one less than the denominator....
On factorising ... got 2 methods
example : 1/(s+2)(s+1) = A/(s+2) + B/(s+1)
1st method ---- lazy method--->residue therom
A = 1/(s+1) |s=-2
= -1
B = 1/(s+2) |s=-1
= 1
Thus 1/(s+2)(s+1) = -1/(s+2) + 1/(s+1)
2rd method ----- comparision
1/(s+2)(s+1) = A/(s+2) + B(s+1)
1/(s+2)(s+1) = [A(s+1) + B(s+2)] / (s+2)(s+1)
Compare the numerator since demonator is the same :
1 = A(s+1) + B(s+2)
Compare the s order term :
0s = As + Bs
A = -B ----- Equ 1
Compare the constant term :
1 = A +2B ------ Equ 2
sub 1 into 2,
B =1
And, A = -1
Thus, 1/(s+2)(s+1) = -1/(s+2) + 1/(s+1) -
oh okie. thanx!
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haha... I already totally forgotten Laplace Transformation
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= inverse laplace{(3/s)(g(s)} ---->where g(s) = 1/(s^2+9)
this one correct meh? i mean, with relation to the question....
eagle help! -
me totally forgot liao... no time now to revise... unless u can wait till sunday... I'm filled to the brim with workOriginally posted by hiphop2009:this one correct meh? i mean, with relation to the question....
eagle help! -
hahaha...it is ok....my maths exam finished liaoOriginally posted by eagle:me totally forgot liao... no time now to revise... unless u can wait till sunday... I'm filled to the brim with work
jia you for ur work! -
hip is engineering student ??
tat paper looks like eg3 to me .... -
yeah. eg3? u from uni or poly?Originally posted by d3athy:hip is engineering student ??
tat paper looks like eg3 to me .... -
from poly ... yr3 students .. grad soon ... XD