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. :-)