Make up two functions f$1$ and f$2$ that have the same Laplace transform. Do not think profound thoughts.

f$1($t$)=1$

and

f$2($t$)=$

$0,$t $0,$t $11,$t $=0$

f$1($t$)=1$

and

f$2($t$)=$

$1,0$ t $<10,1$ t

$$

f$1($t$)=1$

and

f$2($t$)=$

$0,0$ t $<11,1$ t

f$1($t$)=1$

and

f$2($t$)=0$

f$1($t$)=1$

and

f$2($t$)=$

$1,$t $0,$t $10,$t $=0$