In this paper, the longitudinal vibrations of a follower which is the linear active component of a cam mechanism is studied as if it has a constant cross section. The basic Bernoulli method is applied to solve the partial differential equation which is supplied by taking the viscous damping factor into consideration and by adding a new term. For the first time, in addition to the viscous damping, in this investigation, the internal damping term has been imposed to the motion of the follower. The resultant integration constants are determined by using the boundary conditions, and the eigen frequencies are calculated. As a result, two different families of eigen frequencies are remained. The results are formed as computer graphics to be easily understandable.