A particle of mass \(m\) is initially at rest on a frictionless horizontal surface. Starting at time \(t = 0\), a horizontal force directed along the positive \(x\)-axis is applied to the particle with a time-dependent magnitude given by \(F(t) = F_0 \sin(\omega t)\), where \(F_0\) and \(\omega\) are positive constants. The force acts until \(t = \dfrac{\pi}{\omega}\), at which point it drops to zero. Which of the following expressions represents the speed of the particle at time \(t = \dfrac{\pi}{\omega}\)?