Figure Q1 shows a three-degree-of-freedom spring-mass system. If all the masses move to the right direction; a.Construct the free body diagram and develop the equation of motion for each mass. b.Write the equation of motion for the system in matrix form such that it is complete with all parameter values. c.Estimate the natural frequencies of the system where the spring coefficient, k1 = k2 = k3 = k4 = 127 N/m and the masses, m1 = m2 = m3 = 17 kg. d.Determine the mode shapes of the system. Assume x1=1 in modal vector Note: No need to sketch the mode shape diagram

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Free undamped vibrations

Whenever an object/system displaces in either side of its equilibrium position with the help of an external/internal means, then the object/system moves regularly or randomly on both sides of its equilibrium position. This motion is called vibration. Generally, there are three types of vibration: longitudinal vibration, transverse vibration, and torsional vibration.