- #1
Derill03
- 63
- 0
I am asked to find inverse laplace of (3s+5)/(s^2-6s+25)
I do partial frac and get (3s)/((s-3)^2+16) + (5/(s-3)^2+16)
I do the translation and get [(3s)/s^2+16 + 5/(s^2+16)]*e^3t
My final answer is e^3t[3cos(4t) + 5/4sin(4t)]
but the book says the sin term should be 7/2sin(4t)? I say 5/4 because a 4 needs to be in numerator to make use of the table for k/(s^2+k^2) so if you multiply 5 by (5/4) the 4 can be in numerator as 4/(s^2+16) because it will cancel and be the original 5.
I just need to know how the 7/2 gets in the sin term and why its not (5/4)?
I do partial frac and get (3s)/((s-3)^2+16) + (5/(s-3)^2+16)
I do the translation and get [(3s)/s^2+16 + 5/(s^2+16)]*e^3t
My final answer is e^3t[3cos(4t) + 5/4sin(4t)]
but the book says the sin term should be 7/2sin(4t)? I say 5/4 because a 4 needs to be in numerator to make use of the table for k/(s^2+k^2) so if you multiply 5 by (5/4) the 4 can be in numerator as 4/(s^2+16) because it will cancel and be the original 5.
I just need to know how the 7/2 gets in the sin term and why its not (5/4)?