The equation of motion for free vibration of the triple pendulum shown in Fig I are given by: [3 2 1a [3 0 0]e ml 2 2 10,+ mgl 0 2 0 0 0 10, 1 11 Assuming a solution of the form: 0(0) = 0, cos(or), i= 1,2,3, Where e, is the amplitude of 0,1), wis the natural frequency and t is time, derive the (i) problem into standard eigenvalue problem for finding the natural frequencies of vibration (a). (ii) Write a Matlab / Octave program to determine the natural frequencies of vibration and their eigenvector. Compare the eigenvalue and eigenvectors with analytical method. Write a program in Matlab / Octave to execute a power method and inverse power method to determine the largest eigenvalue and smallest eigenvalue respectively with their Eigenpair. Discuss on your findings and observations for (iii) and (iv). Develop a Matlab/Octave program to plot the mode shapes vs time for two different initial conditions. Assuming length,l is 0.5m, g=9.81m's mass =2kg. Use initial condition (IC) [10, 10, 10]" and another IC as in the study case. What method would you use to verify the computation of Matlab program in question (iv). Verify the output of your program and discuss on your findings. (ii) (iv) (v) Figure 1: Triple-Pendulum Sample output of plotting mode shapes vs time va. time, t, (0)-0.35, 0.00, o.00, o.27. -0.31, 0.24, Mass, Masa, Mase 10 Time Mode shapes, w-2.86, 6.71, 11.11, Mode, Mode, O.5 Mode o datat data2 dataa Elements (peds Mode ampitude