Problems

$7\mathrm{.}1.$ Terminal Speed. One way to determine the viscous drag parameter $$ is to apply a steady force $F$ to a particle of mass $M$ and measure its mean terminal speed $v_d.$

a$.$ Express $$ in terms of $F,M,$ and $v_d.$

b$.$ Use the fluctuation$-$dissipation theorem to express the fluctuation parameter ${}^2$ in terms of $kT,F,M,$ and $v_d$ where $T$ is the fluid temperature.