We can use the period of the motion to determine the speed of the particle in terms of the radius of the circular path: \[\begin{aligned} v = \frac{2\pi R}{T}\end{aligned}\] and then use the equation ...We can use the period of the motion to determine the speed of the particle in terms of the radius of the circular path: \[\begin{aligned} v = \frac{2\pi R}{T}\end{aligned}\] and then use the equation for the cyclotron radius to relate this to the charge-to-mass ratio of the particle: \[\begin{aligned} R &= \frac{mv}{qB}\\ &= \frac{2\pi R m}{qBT}\\ \therefore \frac{q}{m} &= \frac{2\pi}{BT} \end{aligned}\]
