Abstract: The analytical solution of movement of particle under the combined two and four power potential is obtained. The displacement of particle is expressed in term of Jacobi elliptical function. The trajectory of particle under two perpendicular potentials, i. e. , the generalized Lissajou＇ s figures, are also discussed and given.

Key words: two and four power potential, elliptical function, Lissajou＇ s figure