Abstract: Additive manufacturing systems especially 3d printers are made by rigid links which provide sufficient stiffness to give motion to 3d printing head system which are moving at very high speed &acceleration. It has been found out that high-speed manipulators generate vibration problem and 3dprinting head is one of them which encounter significant vibration at high speed and acceleration. Therefore, evolution in mathematical control system is necessary for effective vibration suppression and to allow fast motion of 3d printing head at high speed and acceleration. In this paper we develop experiment where we measure the resonance frequency of our bed swinging 3d printer and with graph we optimized it with mathematical system which allows printer to run 140% faster speed and over 600% higher acceleration with same quality and precision. Keyword: 1. Additive Manufacturing, 2. Complex system development, 3. Mechatronics, 4. Robotics, 5. Physics. 6. Advanced engineering mathematics 7. High speed manipulators.