1. A point mass m is supported at the end of a cantilever beam with the length of L and the flexural stiffness of EI as shown in Figure 1. The small static deflection of 8 at the end of the beam is obtained as 8 = PL/3E1 when the external static load of P is applied to the mass. Ignore the mass of the beam. Solve the following problems for the given conditions: (a) When the mass of the beam is ignored, the beam is behaving as a spring. Find an equivalent spring constant for the beam. (b) With the equivalent spring constant and the given mass, draw an equivalent spring mass system. In this system, there is no external excitation force. (c) For the equivalent spring mass system, draw a free-body diagram and obtain the EOM for the displacement of Y. (d) Determine the expression of the natural frequency. El: Bending stiffness L Figure 1: Cantilever beam. Point mass Y m