  We study a class of integrodifferential equations and related ordinary
differential equations for the initial value problem of a rigid sphere falling
through an infinite fluid medium. We prove that for creeping Newtonian flow,
the motion of the sphere is monotone in its approach to the steady state
solution given by the Stokes drag. We discuss this property in terms of a
general nonautonomous second order differential equation, focusing on a
decaying nonautonomous term motivated by the sedimenting sphere problem.
