the vibration of axially moving materials with arbitrarily varying length has received increased attention due to both the interesting behaviours of such systems and the many applications such as deep mine hoisting systems, high-speed elevator systems and robotic arms in a prismatic joint. vibration control is needed for such system; especially when there are safety, speed, and precision concerns. the model governing vibration of such systems is time varying. control of time-varying systems poses many challenges. the objective of this research is to develop an experimental system to study the dynamics of a travelling cable with variable length and to test control strategies for vibration suppression. in this research, an experimental system is developed, which includes a travelling cable apparatus, a signal conditioning circuit board, a data acquisition board, a computer system, and sensors. the mathematical models of the lateral vibration of stationary and axially moving cables are presented. computer simulations are performed to understand the dynamics of the travelling cable. a preliminary testing of the experimental system is preformed boundary control method is used to suppress the vibration of the cable. two closed-loop feedback control systems, direct velocity feedback control and observer output feedback control with optimal feedback gains, are designed to suppress the vibration of the stationary cable. both control systems are simulated by computer and tested by experiment. an observer-based feedback control system with variable optimal feedback gains is designed to suppress the vibration of the travelling cable. the performance of the controller is tested using computer simulations.