Laplace Transforms

Laplace Transforms of e^at

• 1/s+a

• 1/s-a

Laplace Transform of sin at

• s/s²+a²

• a/s²-a²

• a/s²+a²

Laplace Transform of tⁿ

• n!/sⁿ⁺¹

• n!/sⁿ

• (n-1)!/sⁿ⁺¹

Laplace Transform of cosh at

• a/s²+a²

• s/s²-a²

• s/s²+a²

If L[f(t)]=φ(s), L[e^atf(t)]=

• φ(s-a)

• φ(s+a)

Laplace Transform transforms a function from

• $f\left(t\right)\ to\ F\left(s\right)$

• $F\left(s\right)\ to\ f\left(t\right)$

• $f\left(t\right)\ to\ f'\left(t\right)$

• $f"\left(t\right)\ to\ f'\left(t\right)$

Which one is the correct definition of Laplace Transform?

• $F\left(s\right)=\int_0^{\infty}e^{-st}f\left(t\right)dt$

• $F\left(s\right)=\int_0^tf\left(t\right)g\left(t-u\right)$

What is the Laplace Transform for  $f\left(t\right)=t^3$  ?

•  $\frac{1}{s^3}$  

•  $\frac{2}{s^3}$  

•  $\frac{6}{s^4}$  

•  $\frac{3}{s^3}$  

• 0.2

• 0.1

• 5

• 3.3