This image consists of 4 different photos together , top section is problem number 4,left middle section is questions, left lower section is problem number 2, right section is problem number 3

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Problem T-13: Eigenvalue problem for system with rigid mode For the system shown in Figure T-13 [a] Find stiffness and mass matrix of the system. [b] Solve the eigenvalue problem, the the second component is 1,0 Use the following data: m1=1 kg, Figure T-13: 2-dof Free-Free system and normalize eigenvectors SO m2-3 kg, K1-300 N/m. M. Ansers to Problem T-13 [a] stiffness and mass K=300 -300 M = 1 O [b] -300 300 0 3 M matrix of the system. Solve the eigenvalue problem Eigenvalues-[0 400] Eigenvectors 1 1 -3 1 Problem 2: File-A, Problem 3.8 Use m-2 kg and k-800 N/m [1] Solve the eigenvalue problem by eig. [2] Find response due to given initial conditions use mode superposition use eigenvectors computed by eig [3] Find response due to given initial conditions use mode superposition use eigenvectors computed longhand solution given in the answers. [4] Are rhe solutions of Parts [2] and [3] the same? Problem 3: File-B, Problem T-1. Problem 4: File-B, Problem T-13. 3.8 For the 3-dof system shown in Figure P.3.6, [a] Compute te natural frequencies and the associate mode shape of the system [b] Find the responses of the system due to the initial displacements {0 0 1) and initial velocities: {0 0 0}. Two DOF Problems T1 to T-15 Problem T-1:Eigenvalue problem For the 2-dof system shown in Figure T-1, use the following data: k1-400; k2-150;,m1-2,m2=1. [a] Derive mass and stiffness for this system [b] Solve eigenvalue problem by longhand calculation Normalize the eigenvectors so that For first mode first component=1 and second component-1, for the 2nd mode. [c] re-norlalize the eigenvectors by mass-normalization. [d] Let Phil and Phi2 be the modes computed in Part [b] remormalize the eigenvectors to RP1 and RP2 to make RP1' *K*RP1-100, RP2 *M*RP2=22. [e] Compute GM1-RP1 *M*RP1, GK2=PR2**K*PR2. [f] Re-compute GM1 and GK2 use results of part [a] to [c] i.e, without performing the matrix products [g] validate the solution by solving the eigenvalue problem by Matlab function 'eig'. If they are not the same (ignore the numerical difference), why? Are they both correct solutions of the eigenvalue problem? Ans: k/2 k/2 k m k/2 13 k/2 xy(f) x(1) xi(f) k www Figure P3.6 , 0.518,=. , {0} = {1 1+3 2+3} =1.414, {0}={1 1 -1}' m 32 (0) = {1 1-3 2-3} =1.932 x (1) + { } cos 0,1 x(t) = {0} cos tot (9) cos 0.1+ (x, (1)] 1 2-dof spring-mass system Problem T-13: Eigenvalue problem for system with rigid mode For the system shown in Figure T-13 [a] Find stiffness and mass matrix of the system. [b] Solve the eigenvalue problem, the the second component is 1,0 Use the following data: m1=1 kg, Figure T-13: 2-dof Free-Free system and normalize eigenvectors SO m2-3 kg, K1-300 N/m. M. Ansers to Problem T-13 [a] stiffness and mass K=300 -300 M = 1 O [b] -300 300 0 3 M matrix of the system. Solve the eigenvalue problem Eigenvalues-[0 400] Eigenvectors 1 1 -3 1 Problem 2: File-A, Problem 3.8 Use m-2 kg and k-800 N/m [1] Solve the eigenvalue problem by eig. [2] Find response due to given initial conditions use mode superposition use eigenvectors computed by eig [3] Find response due to given initial conditions use mode superposition use eigenvectors computed longhand solution given in the answers. [4] Are rhe solutions of Parts [2] and [3] the same? Problem 3: File-B, Problem T-1. Problem 4: File-B, Problem T-13. 3.8 For the 3-dof system shown in Figure P.3.6, [a] Compute te natural frequencies and the associate mode shape of the system [b] Find the responses of the system due to the initial displacements {0 0 1) and initial velocities: {0 0 0}. Two DOF Problems T1 to T-15 Problem T-1:Eigenvalue problem For the 2-dof system shown in Figure T-1, use the following data: k1-400; k2-150;,m1-2,m2=1. [a] Derive mass and stiffness for this system [b] Solve eigenvalue problem by longhand calculation Normalize the eigenvectors so that For first mode first component=1 and second component-1, for the 2nd mode. [c] re-norlalize the eigenvectors by mass-normalization. [d] Let Phil and Phi2 be the modes computed in Part [b] remormalize the eigenvectors to RP1 and RP2 to make RP1' *K*RP1-100, RP2 *M*RP2=22. [e] Compute GM1-RP1 *M*RP1, GK2=PR2**K*PR2. [f] Re-compute GM1 and GK2 use results of part [a] to [c] i.e, without performing the matrix products [g] validate the solution by solving the eigenvalue problem by Matlab function 'eig'. If they are not the same (ignore the numerical difference), why? Are they both correct solutions of the eigenvalue problem? Ans: k/2 k/2 k m k/2 13 k/2 xy(f) x(1) xi(f) k www Figure P3.6 , 0.518,=. , {0} = {1 1+3 2+3} =1.414, {0}={1 1 -1}' m 32 (0) = {1 1-3 2-3} =1.932 x (1) + { } cos 0,1 x(t) = {0} cos tot (9) cos 0.1+ (x, (1)] 1 2-dof spring-mass system