Final Report – 3DOF System AnalysisStructural DynamicsAssumptionA three-story shear frame is shown in the Figure 1.N∙sec2/m = tonne (metric ton)=1 kN∙sec2/m=100GPah=5mI=4×10-5 m-4==1.5, ========2, =1.5,=calculating the natural frequencies and mode shapesMass MatrixStiffness MatrixInfluence Coefficients Method: Each column of the stiffness matrix, e.g. column j, corresponds to DOF j. To obtain values of each column, a unit displacement is imposed at DOF j and zero at the others. The stiffness influence coefficients are Kij. The forces necessary at top and bottom of each story to maintain the deflected shape are expressed in terms of story stiffness, ki.1st story stiffness:2nd story stiffness:3rd story stiffness:Stiffness MatrixEquation of MotionThe natural vibration frequencies and modes of the system, ,