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The natural frequencies of vibration (in Hz) for a cantilevered beam of length L, elastic modulus E, density p, cross-sectional area A, and cross-sectional area moment is given by, (b) fn (1) (ii) (iii) = P 2L where pn is the n-th root of cosh(x) cos(x) + 1 = 0. (a) Approximate the first three positive roots p and hence determine the respective natural frequencies of vibration. Assume L = 0.25m, E = 200 10 N/m, I = 1.667 10-m, p = 7800kg/m and A = 2 x 10-5m. Clearly state: n = 1,2,... the root-solving algorithm that you are using to obtain p n' the starting guess(es) or initial search interval, and, the convergence criterion i.e the tolerance or percentage error in successive approximations. Write an approximation of the asymptotic expression for fn. Compute the percentage error between the approximate value (based on the asymptotic approximation) and the values that you computed in part (a) for the natural frequencies.