w(xit) b) (x7) EI L Consider a beam as shown with a fixed left end and a free right end. The product El = 1 GPa- mm4 and the density of the beam per unit length is 100 kg/m. The beam's length is 10 m. 1. Using one element for the entire beam, calculate the resonance frequencies and mode shapes by hand using modal analysis and a mass matrix that takes rotary inertia and shear deformation into consideration (see lecture 22 28 Nov 2023 for more information on this). 2. Using four elements for the entire beam, equally spaced with 2.5 m per element, calculate the resonance frequencies and mode shapes using modal analysis and the same mass matrix as for part 1 for each element. Note that assembly of the global mass matrix proceeds exactly the same as for the global stiffness matrix.