Laplace transform (translation on the s-axis)

[PhysicsCollegeGirl]

Homework Statement

L-1{[(2s-1)]/[(s^2)(s+1)^3]}

Homework Equations

L{f(t)e^(at)}=F(s-a)

The Attempt at a Solution

I have tried million ways but the different exponents in the denominator are throwing me off.
The other problem is that I cannot use partial fractions, the homework instructions require me to use translation in the s-axis.
But now I am thinking that I have to use partial fractions anyway? Can someone just tell me if there is a way to solve it without using partial fractions, and I will keep at it. If there is not, I can move on with my life in peace. Thank you!

 

[LCKurtz]

Homework Statement

L-1{[(2s-1)]/[(s^2)(s+1)^3]}

Homework Equations

L{f(t)e^(at)}=F(s-a)

The Attempt at a Solution

I have tried million ways but the different exponents in the denominator are throwing me off.
The other problem is that I cannot use partial fractions, the homework instructions require me to use translation in the s-axis.
But now I am thinking that I have to use partial fractions anyway? Can someone just tell me if there is a way to solve it without using partial fractions, and I will keep at it. If there is not, I can move on with my life in peace. Thank you!

I haven't worked it myself, but judging from what the problem looks like, I would write it as$$
\frac{2s-1}{s^2}\cdot \frac 1 {(s+1)^3}$$and use the convolution of the inverses of the two fractions. The second one would give you a chance to use your translation formula.

 

[Ray Vickson]

Homework Statement

L-1{[(2s-1)]/[(s^2)(s+1)^3]}

Homework Equations

L{f(t)e^(at)}=F(s-a)

The Attempt at a Solution

I have tried million ways but the different exponents in the denominator are throwing me off.
The other problem is that I cannot use partial fractions, the homework instructions require me to use translation in the s-axis.
But now I am thinking that I have to use partial fractions anyway? Can someone just tell me if there is a way to solve it without using partial fractions, and I will keep at it. If there is not, I can move on with my life in peace. Thank you!

I doubt that you have tried more than 10,000 ways. Anyway, if I were doing it I would first expand it into partial fractions, then use the "translation" property on 3 of the 5 terms.

Whether that is OK depends on whether your instructions imply that you must use only the translation property and nothing else, or whether it just requires you to use translation somewhere in the solution. That is something only you can decide.