The above figure shows a mechanical system with n-number of masses. Considering the undamped system, write a computer to find natural frequencies and corresponding mode shapes. The program should allow to enter the value of $\mathrm{n} $ and accordingly it constructs the mass, stiffness and damping matrices, and solves the natural frequencies and mode shapes. Using this program, study the following cases (find the eigenvalues and eigenvectors), you can select your own values of $\mathrm{m} $ and $\mathrm{k}$. (a) For $\mathrm{n}=3, \mathrm{-m} _{1}>\mathrm{m}_{2}>\mathrm{m}_{3}$ and $\mathrm{k}_{1}\mathrm{m}_{2}>\mathrm{m}_{3}>\mathrm{m}_{4}>\mathrm{m} _{5}>\mathrm{m}_{6}>\mathrm{m}_{7}>\mathrm{m}_{8}>\mathrm{m}_{9}>\mathr m{m}_{10}$ and $\mathrm{k}_{1}=\mathrm{k}_{11}=0, \mathrm{k}_{1}=\mathrm{k}, \mathrm{i}=1: \mathrm{n} $ (d) for $\mathrm{n}=50, \mathrm{-m}_{\mathrm{i}}=\mathrm{m} $ and $\mathrm{k}_{\mathrm{i}}=\mathrm{k}, \mathrm{k}_{51}=0, \mathrm{i}=1: \mathrm{n} $ Comment on your results. CS.VS. 1145 The above figure shows a mechanical system with n-number of masses. Considering the undamped system, write a computer to find natural frequencies and corresponding mode shapes. The program should allow to enter the value of $\mathrm{n} $ and accordingly it constructs the mass, stiffness and damping matrices, and solves the natural frequencies and mode shapes. Using this program, study the following cases (find the eigenvalues and eigenvectors), you can select your own values of $\mathrm{m} $ and $\mathrm{k}$. (a) For $\mathrm{n}=3, \mathrm{-m} _{1}>\mathrm{m}_{2}>\mathrm{m}_{3}$ and $\mathrm{k}_{1}\mathrm{m}_{2}>\mathrm{m}_{3}>\mathrm{m}_{4}>\mathrm{m} _{5}>\mathrm{m}_{6}>\mathrm{m}_{7}>\mathrm{m}_{8}>\mathrm{m}_{9}>\mathr m{m}_{10}$ and $\mathrm{k}_{1}=\mathrm{k}_{11}=0, \mathrm{k}_{1}=\mathrm{k}, \mathrm{i}=1: \mathrm{n} $ (d) for $\mathrm{n}=50, \mathrm{-m}_{\mathrm{i}}=\mathrm{m} $ and $\mathrm{k}_{\mathrm{i}}=\mathrm{k}, \mathrm{k}_{51}=0, \mathrm{i}=1: \mathrm{n} $ Comment on your results. CS.VS. 1145