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Learning Outcomes 1.Understand the fundamentals of mechanical vibrations and how mechanical vibrations affect design. 2.Develop expressions for and calculate the natural frequencies of components using Newton's second law and energy methods. 3.Derive theoretical models for the response of a system undergoing mechanical vibrations for undamped, under-damped, critically damped and over-damped systems. 4.Investigate system stability and design components to operate away from natural frequencies. 5.Determine the response of a system subjected to harmonically excited vibrations and general forcing conditions. 6.Evaluation of the system response to mechanical vibrations using Laplace transforms to derive the response of a system. 7.Introduction to multi degree of freedom analysis. 8.Implementation of theoretical models for system response in MATLAB. 9.Measurement of mechanical vibrations and component natural frequencies.