The characteristic equation of a 3 DOF spring mass system as shown in Figure 1 can...

 

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The characteristic equation of a 3 DOF spring mass system as shown in Figure 1 can be further developed as a set of simultaneous equations: k ин k k m M Figure 1 2V1 V2 = 0 -V1 2V2 V3 = 0 -V2 + V3 = 0 (a) Write the simultaneous equation in a complete matrix form of [A][V]= 0. (b) Find the smallest eigenvalue and its corresponding eigenvector using Inverse Power Method. Use v(0) = (010) and iterate until 2k+1-λk <0.05 (c) Find the largest eigenvalue and its corresponding eigenvector using Power method. Use v(0) = (010) and iterate until 2k+1-λk| <0.05 The characteristic equation of a 3 DOF spring mass system as shown in Figure 1 can be further developed as a set of simultaneous equations: k ин k k m M Figure 1 2V1 V2 = 0 -V1 2V2 V3 = 0 -V2 + V3 = 0 (a) Write the simultaneous equation in a complete matrix form of [A][V]= 0. (b) Find the smallest eigenvalue and its corresponding eigenvector using Inverse Power Method. Use v(0) = (010) and iterate until 2k+1-λk <0.05 (c) Find the largest eigenvalue and its corresponding eigenvector using Power method. Use v(0) = (010) and iterate until 2k+1-λk| <0.05