Question 1 Derive the set of differential equations for a three mass-four spring system (see the figure below) that describes their motion as a function of time. Write the three differential equations a) Note each equation has been divided by the mass. k,I k3 n- E m b) Solve for the eigenvalues and natural frequencies for the following values of mass and spring constants: ki kkk 240 N/m, and mi m2 ma 40 kg. (Round the final answers to four decimal places and write them as displayed in MATLAB) c) Produce a plot to identify the principle modes of vibration. Refer to Figure 13.4 in the text for an example of such a plot for a two mass-three spring system