f(t) = cos(wt)
L(f(t)) = \int_0^\infty (cos(wt)e^{-st}) dt
w = cos(wt) => dt = -\frac{1}{w}e^{-st}dt
\int f = e^{-st} v = -\frac{1}{w}e^{-st}cos(wt) dt
\int e^{-st} (-\frac{1}{w}e^{-st}sin(wt)) dt
\int e^{-st} (-\frac{1}{\lambda}e^{-st}) dt
\int e^{-st} (\frac{w^2}{\lambda^2}) \int_0^\infty e^{-st}cos(wt)dt
\int_0^\infty e^{-st}cos(wt)dt = \int_0^\infty e^{-st} e^{-wt} dt
\int_0^\infty e^{-st} e^{-mt} dt = \int_0^\infty e^{-nt} dt
\frac{M}{\lambda^2 + w^2} \int_0^\infty cos(wt)e^{-nt} dt
