In this paper, we show the numerical integration method of solving Lagrange-Maxwell equation by using the symplectic Runge-Kutta (R-K) method, and numerically study the motion of the plate in an RLC circuit spring coupled system and the current changes. Its result is consistent with that obtained by the traditional R-K method, which demonstrates symplectic integration algorithm is reasonable and effective in studying the electro-mechanical systems. And on this basis, the form invariance of Noether sense is studied by using the symplectic Runge-Kutta method.