This paper details pendulum characteristic linked with a vertical automatic washing machine. At first, a non-linear mode provided in [2] is linearized at its static equilibrium position and ingredients of its Jacobian matrix are analyzed. Second, the pendulum mode born with the machine is obtained by an eigensolution, and factors contribute to this mode are discussed. Third, relationships between the pendulum mode and a damp coefficient in the suspenders are found based on simulation results and pendulum characteristics are analyzed. The existence of the critical damp coefficient is discussed based on energy, factors affect it are then considered. Fourth, the bisection method is employed to determine the critical damp coefficient in a particular washing machine; relationships between the damp coefficient and radius of unbalance under different rotation speed are then fitted by several second order polynomials. The existence of the critical damp coefficient is supported through experiment and effect of the hydraulic balancer is finally discussed.