Task 4: Equations of motion for 2 DOF system (20% of 100%) Specification: Derive the equations of motion about the equilibrium position of the system below using the Lagrange's approach and evaluate the influence of the linear spring (stiffness) on the undamped natural frequencies. Define all required parameters, a coordinate system, generalised coordinates, positive orientations, etc. For the parametric study, define your own suitable and meaningful parameter values. Note: both horizontal pendulums have massless arms Torsional DOF 2 Mass 2 Wall and rigid column spring 2 Equilibrium position Linear spring Gravity DOF 11 Equilibrium position Torsional Mass 1 spring 1 1.6 m Present the following Results and Discussion points: In first figure shown in Results, include a picture of the system in the deformed configuration with the suitable coordinate frame of reference and positive orientations of the generalised coordinates which you use to form the system Lagrangian. Annotate the figure to make these decisions clear. In Results, provide the derived and complete Lagrangian and describe the individual energy terms. In Results, provide the mass and stiffness matrix formulas of the linearised system. In the second figure shown in Results, include the visualisation (drawing) of the mode shapes in terms of their characteristic properties. In the third main figure shown in Results, include the graph which shows the changes of the undamped natural frequencies of the system when varying the linear spring stiffness between the 0 value and very high value of the spring stiffness. One paragraph in your Discussion should comment briefly on the influence of gravity in the final linearised form of the resulting EoMs. One paragraph in your Discussion should aim to interpret or explain the changes and trends in the natural frequencies when varying the linear stiffness.