Three charged particles initially have identical masses, charges, and speeds and are traveling perpendicular to the same magnetic field. Because they are all in the same magnetic field and have identical masses and charges, all particles have the same initial cyclotron frequency and revolve with the same period \(T\). The speed of particle 1 is doubled; particle 2 enters a region in which the magnetic field has been reduced by a factor of 2 ; and particle 3 collides with and sticks to a neutral particle of the same mass, causing a change in speed. Determine the new period of each particle in terms of the initial period \(T\).