Q5. N coupled harmonic oscillators ( 25 points) Consider a 1D chain of N blocks with masses m connected by springs with spring constants k. At its ends, the chain is attached to fixed wall by springs with spring constants Kb. The displacement of the j-th block from its equilibrium position is denoted as uj. Assume only longitudinal motions are allowed. (a) Write down the equation of motion of the j-th block in the chain. This equation holds for all the blocks except those at the two boundaries. Write down the equation of motion for the blocks at the two boundaries. (b) Assume a trial solution uj(t)=ajeit and substitute it into the equations of motion in part (a). Express the sets of coupled equations in matrix form of Dx=2x, where D is a NN matrix and x=(a1,a2,aN)T (c) Let N=6. Write a program that calculates the characteristic frequencies as a function of k/Kb. Plot your results