Elementary Vibrations Experiment

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Abstract This was an academic laboratory report which was assigned to an experiment accomplished at February 24, 2011. The main objective of this experiment was to assemble a vibrating system and measure its natural frequency in simple harmonic motion by comparing the theoretical and experimental natural frequencies of a simple spring-mass-pulley system. Table of Contents Abstract 1 1. Introduction 2 2. Theory 4 3. Results 5 4. Discussion 7 5. Conclusions 7 6. References 8 Introduction The experiment was aiming at comparing the calculated and measured natural frequencies of a simple spring-mass-pulley system. The calculated natural frequencies were based on the assumption that the whole system undergoes simple harmonic oscillation. As long as the system had no energy loss the mass would continue to oscillate. On the other hand, the measured natural frequency was based on an equation provided using variables which could be measured directly. Since there was always energy loss in actual practice situation, the calculated natural frequency should be theoretically lower than directly measured natural frequency. In conclusion, this assumption as mentioned above would be proven by analyzing the results. Description of Apparatus Fig.1 A schematic diagram of the main apparatus. Figure 1 showed the plane view of the spring-mass-pulley system that was used in this experiment. As shown in the diagram, the apparatus consisted of a spring, a pulley, a mass less rope (light cord) and a weighted body. The pulley were fixed by the spring to the ceiling as well as fixed by one end of the rope to the ground while the body hanged freely at the other end. The vertical motion of body had shown the existence of the vertical acceleration of the body as well as the angular acceleration of the pulley about its centre. Theoretical Value – Spring

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