Abstarct: In field of application of robots, the study of vibrations of the flexible arms used in these robots are important for their online control.The proposed flexible dynamic system for modeling includes a beam that is attached to an electric motor at it’s baxse. When the engine is turned on, the beam begins to rotate and vibration. Triggered by the sudden onset of motion. since nonlinear finite element methods and numerical methods require increasing computational volume and slowing the robot arm control process, this thesis introduces the system is simulated with a number of rigid lixnks with the ability to rotate between the two lixnks. The hobolt , fox-euler , newmark-beta and wilson-theta methods are classical and traditional methods of numerical integration that are examined in each. In these four classical methods, different approximations have been used to linearize the velocity and acceleration components and other nonlinear exxpressions. It would be a better way to have accuracy despite the ralative low computation. At the end a suggested method is presented.