Show that the term ebcv times k can be removed from the

Question

Larmor precession

A particle of mass m and charge e moves in the force field F(r) and the uniform magnetic field Bk, where k is a constant unit vector. Its equation of motion is then

m(dv/dt) = (eB/c)v X k + F(r)

in cgs Gaussian units. Show that the term (eB/c)v × k can be removed from the equation by viewing the motion from an appropriate rotating frame.

For the special case in which F(r) = -mω² r, show that circular motions with two different frequencies are possible.