Problem 1: Application of the Fixed-Point Iteration Method In class, we have presented the non-dimensional frequency equation, given below, whose roots are related to the natural frequencies of vibration of a cantilever beam. f(a) = 1 + cosh(1) cos(1) = 0 The following iterative algorithm is proposed in an attempt to obtain the roots of the frequency equation using the fixed-point iteration method 1 +1 = + cos(ak) + k, k = 1,2,3,... cosh(k) (In your MATLAB programming, you may replace by x for simplicity.) In the pre-lab, you have already developed a numerical solver for the fixed-point iterative algorithm which will terminate when the relative approximate error is smaller than a user-specified maximum tolerance maxtol or when the number of iterations exceeds a user-specified maximum number of iterations maxitr. a) Show how the above algorithm is derived based on fixed point iteration concept. b) Test your fixed-point numerical solver using an initial guess of x1=4.5, maxtol=0.001, and maxitr=20. Explain why it does not converge to the second root which is very close to the initial guess of 4.5 (use a graphical plot to help your explanation, as needed).