mathstresser
Junior Member
- Joined
- Jan 28, 2006
- Messages
- 134
Find the general solution to
y'' + 9y =g(t), y(0)=0, y'(0)=1 using Laplace Transform.
Express your result in the form of the convolution of g*e where e is the unit impulse response for the system modeled by the above equation.
This is what I did:
(s^2)Y(s)-sy(0)-y'(0) +9[sY(s)-y(0)]
(s^2)Y(s)-s(0)-1 +9[sY(s)-(0)]= g(t)
Y(s)[s^2+9]-1=g(t), =0
Y(s)= s/(s^2+9)= 1/(s^2+3^2)
= cos(3t)
What did I do wrong?
y'' + 9y =g(t), y(0)=0, y'(0)=1 using Laplace Transform.
Express your result in the form of the convolution of g*e where e is the unit impulse response for the system modeled by the above equation.
This is what I did:
(s^2)Y(s)-sy(0)-y'(0) +9[sY(s)-y(0)]
(s^2)Y(s)-s(0)-1 +9[sY(s)-(0)]= g(t)
Y(s)[s^2+9]-1=g(t), =0
Y(s)= s/(s^2+9)= 1/(s^2+3^2)
= cos(3t)
What did I do wrong?