(Solved): vibration Figure Q1 shows a three-degree-of-freedom spring-mass system. If all the masses move to th ...

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. (6 marks) (b) Write the equation of motion for the system in matrix form such that it is complete with all parameter values. (3 marks) (c) Estimate the natural frequencies of the system where the spring coefficient, k? = k? =k3=k4 = 137 N/m and the masses, m = m2 = m3 = 15 kg. (7 marks) (d) Determine the mode shapes of the system. Assume x-1 in modal vector Note: No need to sketch the mode shape diagram (9 marks) m? m? m? Figure Q1