This paper studied the friction damping factors that influence electromagnetic rail launching. An electrical magnetric launcher orbit was simulated into an elastic foundation beam under a movement loading, a mathematical model of beam was established by using Euler beam theory, and the analytic solution of the flexural deflections of an orbit involving exponential functions of the dynamics problem under a simple harmonic pressure was derived with the help of the integral transformation, the inverse transformation and so on. The results of the numerical examples with MATLAB software showed that the elasticity coefficient, the viscous external damping coefficient and the coulomb damping coefficient have different influences on the transient dynamic response. So it provides sufficient theory evidence about the initial value problem of solving a higher order partial differential equation and improving the performance of an electromagnetic emission device.