Figure below shows a 2D cantilevered beam, length (L) 0.1 m, attached to an axial spring with spring stiffness (k) of 500,000 N/m. The square cross section of the cantilever beam measures 0.01 m x 0.01 m. It is manufactured from steel with density (p) 7850 kg/m and modulus (E) 200 GPa. I=1/12 bh, mass = PAL a) Using a consistent mass matrix and using one beam element to model the cantilever beam, write down the equations of motion for the two degrees of freedom system. b) Determine the first two natural frequencies of vibration of the beam. c) Determine the two corresponding mode shapes K 0.1 m (14 marks) (10 marks) (8 marks)