L{sin(wt)} = w/ (s^2 + w^2)
It's a formula.. I didn't do the integration.
find the laplace transform F(s) of f(t) = sin wt
the w is actually supposed to be omega
what i got was
integeral from 0 to infinity of: (sin wt)*(e^-st) dt
then i integrated by parts and obtained a large expression
which involves the limit to infinity of sin and cos ... how do i solve this limit
can someone post a step by step explanation starting from the limit part
By parts, let and . Thus, and
Thus, we have , since (You can take note that sine oscilates bewteen -1 and 1, but approaches zero very quicly. Thus its the term we are most concerned with when evaluating the limit.)
Now, let and . Thus, and
Thus, we now see that since by similar explanation above. Also note that .
Thus, it is now evident that
Keep in mind this is only true when .
Does this make sense?