I need a help for this question #6. I have already given all resource and equation 6.4 which the question need. I will give a 'helpful' rate for your answer.

\f#6. Weighted string with friction We now assume that the particles in the weighted string problem are subject to a. force due to the presence of 'iction. {Imagine the particles are moving in a. medium which o'ers resistance to the motion of the particles.) Assuming the frictional force is proportional to the velocity, the system of differential equations describing the motion is (For T (111- . m (#23 = 3 (\"1+1 - 2% +\"jl) - 'r', J = 1.2.....N (6.52) where 7 is positive and, as before, on = nN+1 = D. 1. Rewrite the system {6.52) in matrix form such that when 7 = 0 the equation becomes identical to the matrix equation (6.4). 2. Assume a solution of the form . u(t) = ew'f (6.53) where f is a column vector independent of t and w is to be determined. For what values of w is (6.53) a solution to the matrix equation derived in part (1)? NOTE: This will not require a complete reworking of the eigenvalues since you may use the information we already have proved about VN to nd the eigenvalues in this new problem. You should not have to solve anything more complicated than a quadratic equation. E'R'ecall that if X is any matrix then X\" is the matrix obtained by taking the complex conjugate of each element in X and then taking the transpose. 6.9. EXERCISES 11 l 3. Explain the signicance of the fact that the w's you obtain are complex numbers. 4. For a large system N 3> 1 explain why you expect some of the allowed We to be purely imaginary. Explain the signicance of this result, i.e. what is the implication for the motion