# Laplace Transform of Integral

• Oct 6th 2009, 05:23 PM
dsprice
Laplace Transform of Integral
Find f(t) if L(f) = 5/[s**2 - 5s]

From this, I can see components of cosh(SQRT(5)t), but the answer in the back of the book is cosh(SQRT(5)t) - 1.

Just not quite seeing how to get there. If anyone can provide guidance (not necessarily the full answer), it will be much appreciated.
• Oct 6th 2009, 06:46 PM
mr fantastic
Quote:

Originally Posted by dsprice
Find f(t) if L(f) = 5/[s**2 - 5s]

From this, I can see components of cosh(SQRT(5)t), but the answer in the back of the book is cosh(SQRT(5)t) - 1.

Just not quite seeing how to get there. If anyone can provide guidance (not necessarily the full answer), it will be much appreciated.

$\displaystyle f(t) = 5 L^{-1} \left[ \frac{1}{s(s - 5)} \right] = 5 L^{-1} \left[ \frac{A}{s} + \frac{B}{s - 5} \right] = 5 (A + B e^{5t})$

where you should be able to get the constants A and B arising from the partial fraction decomposition.
• Oct 7th 2009, 06:08 PM
dsprice
I now see where I messed up...right at the beginning.

Instead of "Find f(t) if L(f) = 5/[s**2 - 5s]"...

...It should have been "Find f(t) if L(f) = 5/[s**3 - 5s]"

I now understand how to work it out.