2. A shaft is modeled as clamped at the left end and on an elastic foundation on the right end. The elastic foundation is represented by a spring with stiffness k. a. Calculate the natural frequencies and mode shapes of the shaft using two beam elements of equal length. b. Compare the results from (a) with those for a clampedhinged shaft. c. Compare the results from (a) with those for a clampedclamped shaft. In cases (b) and (c) there is no elastic foundation supporting the shaft. Use two beam elements for (b) and (c) also. Assume: L = 1 m, E = 100 GPa, A = 10 m, I = 107 m; p=4000kg/m, and k = 2 106 N/m. , E, I, L k