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A three degree of freedom system is shown in Figure. The three masses are each 1 kg and are constrained to move in the directions shown. The three stiffnesses are 5 kN/m, 50 kN/m, and 500 kN/m as shown.
(a) Use one and two degree of freedom approximations to estimate the three natural frequencies of the system in Hz.
(b) Write the equations of motion of the system using matrices.
(c) Using MATLAB or otherwise, calculate the three natural frequencies of the system and the associated mode shapes normalised on the largest value.
(d) Find the principal stiffnesses for the system using the normalised mode shapes.
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