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find A,B,C

Ax+B ?! As+B?!

yes, As+B

i am getting C=1/w^2 , B=0 , A =-1/w^2
are u getting the same ?

did u forget s ?

As+B

w^2 is constant

Oh!!! Sorry!!!

i was trying exactly that...using convolution

\(\int_0^t u(t-u)sin (\omega u)/\omega \:\:du\)
did u reach here ?

and i am getting same answer with convolution also.

also its ,
\(\huge L(u(t)*\frac{sin\omega t}{\omega }) = \frac{1}{s(s^2+\omega ^2)}\)

doubts ? i assume you are trying...

Why is it \( L(u(t)*\frac{sin\omega t}{\omega }) = \frac{1}{s(s^2+\omega ^2)}\) ???

because L[u(t)] = 1/s
and NOT L[1] = 1/s ...

!!!!! How come...

Of course I try first :) Sorry to keep you waiting again!

in the definition its 0 to infinity or -infinity to infinity ??

0 to infinity. That's what I've learnt..

I haven't learnt \(L (u(t)) = \frac{1}{s}\)....

then take it as 1...

\(\int_0^t 1.sin (\omega (t-u))/\omega \:\:du\)
u got this?

I... think I got that..

then its just a normal definite integration problem

didn't get it ?

welcome ^_^