- #1
xVladx
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Homework Statement
Hi all came across this problem whilst doing some revision and i can't work out the answer
Solve the following equation with laplace transformation
Homework Equations
y''+16y = f(t) = { 1 t < pi ] with y(0) = 0 and y'(0) = 0
_____________{ 0 t >= pi ]
The Attempt at a Solution
I find the laplace transform and get:
Y(s) = (1/16s)-(1/(16(s^2+4^2)))-(e^(-pi*s)/(s^2+4^2))
I am kind of stuck when doing the final step since never delt with this type of problem and the sine/cosine transforms.
I come up with y(t)=1/16 - sin(4t)/64 - (sin(4t)* u(t - pi)) /16 but not sure if it is right or how to get it back to the final form.
Any help is appreciated