Originally Posted by
dsprice Find, graph, and discuss the solution of the following:
y'' + y = delta(t - 2pi)
y'(0) = 0
y(0) = 10
where delta is Dirac's delta function
Transforming, we get:
(s^2)Y + Y = e^(-2*pi*s)
(s^2 + 1)Y = e^(-2*pi*s)
Y = [e^(-2*pi*s)]/[(s^2 + 1)]
y(t) = L^-1[Y(s)]
Assuming everything's correct up to this point, I can see sin(t) in the denominator of Y above, but the answer in the back of the book is:
y = 10cos(t) if 0 < t < 2*pi
y = 10cos(t) + sin(t) if t > 2*pi
I really feel uncomfortable with my knowledge of time-shifts, so if someone could please help explain how to get from point A to point B, it'd be much appreciated. Not looking for complete solution, but enough to get this horse to see where the water might be located. :-)