Exponential and Trigonometric Functions

f$\left(\vphantom{ t}\right.$t$\left.\vphantom{ t}\right)$ F$\left(\vphantom{ s}\right.$s$\left.\vphantom{ s}\right)$ = L$\left\{\vphantom{
f}\right.$f$\left.\vphantom{
f}\right\}$$\left(\vphantom{ s}\right.$s$\left.\vphantom{ s}\right)$
eatsin kt ${\dfrac{{k}}{{\left( s-a\right) ^{2}+k^{2}}}}$


eatcos kt     ${\dfrac{{s-a}}{{\left( s-a\right) ^{2}+k^{2}}}}$