How to convert from Laplace Domain to Time Domain?
As per: https://math.stackexchange.com/questions/3485053/how-to-get-partial-fractions-for-this-equation-to-go-from-laplace-to-time-doma

$F(s) = \frac{-2 m k v R}{2mR\left(s-\frac 1{4mR}\left(-mk-\sqrt{m^2k^2-16mkR^2}\right)\right)\left(s-\frac 1{4mR}\left(-mk+\sqrt{m^2k^2-16mkR^2}\right)\right)}$

$F(s) = \frac{-2 m k v R}{2mR}*\frac{1}{\left(s-\frac 1{4mR}\left(-mk-\sqrt{m^2k^2-16mkR^2}\right)\right)\left(s-\frac 1{4mR}\left(-mk+\sqrt{m^2k^2-16mkR^2}\right)\right)}$

$F(s) = - k v *\frac{1}{\left(s-\frac 1{4mR}\left(-mk-\sqrt{m^2k^2-16mkR^2}\right)\right)\left(s-\frac 1{4mR}\left(-mk+\sqrt{m^2k^2-16mkR^2}\right)\right)}$

Then I can use:

$\frac{1}{(s+a)(s+b)} = \frac{e^{-at}-e^{-bt}}{b-a}$

And that should do it!