A small bead of mass \(m\) is threaded onto a vertical guide wire.

The bead is subjected to a downward gravitational force, a constant upward magnetic force of magnitude \(F_0\) (where \(F_0 < mg\)), and an upward drag force of magnitude \(bv\), where \(v\) is the bead's downward speed and \(b\) is a positive constant. At time \(t = 0\), the bead is projected vertically downward with an initial speed \(v_0\). Which of the following expressions represents the downward speed \(v(t)\) of the bead as a function of time \(t\)?