m, Ic d y2 m m When y = 0 and y = 0, the spring...

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m, Ic d y2 m m When y = 0 and y = 0, the spring is unstretched and the point G is vertically aligned below C (as shown in the figure). Answer all the following parts (a, b, c, d and e) a) In your PDF solutions, show that the nonlinear equations of motion of the system in y and y are the following: 12.0.1+93-y1+93-y2 = -117.72+ F(t) 17.33.2 +93-1 +93-y2 + 39.24-sin(y2/1.8)=-117.72 b) In your PDF solutions and starting from the equations of motion given in part (a), show that the position y = -1.2658 m and y = 0 m is a stable equilibrium position (you need to show that the given position is an equilibrium position and also that it is stable) c) In your PDF solutions, linearise the equation of motion given in part (a) around the equilibrium position given in part (b). Then find and report here the numerical values of the Mass and Stiffness matrices M = kg kg kg kg K = N/m N/m N/m N/m d) Find the steady state amplitude of vibration for y and y in millimetres. Steady state vibration amplitude of y = Steady state vibration amplitude of y2 = mm mm e) In your PDF solutions, draw the particular solution (steady state solution) y,p(t) and y2,p(f) as a function of time and annotate your diagrams with the key quantities. m, Ic d y2 m m When y = 0 and y = 0, the spring is unstretched and the point G is vertically aligned below C (as shown in the figure). Answer all the following parts (a, b, c, d and e) a) In your PDF solutions, show that the nonlinear equations of motion of the system in y and y are the following: 12.0.1+93-y1+93-y2 = -117.72+ F(t) 17.33.2 +93-1 +93-y2 + 39.24-sin(y2/1.8)=-117.72 b) In your PDF solutions and starting from the equations of motion given in part (a), show that the position y = -1.2658 m and y = 0 m is a stable equilibrium position (you need to show that the given position is an equilibrium position and also that it is stable) c) In your PDF solutions, linearise the equation of motion given in part (a) around the equilibrium position given in part (b). Then find and report here the numerical values of the Mass and Stiffness matrices M = kg kg kg kg K = N/m N/m N/m N/m d) Find the steady state amplitude of vibration for y and y in millimetres. Steady state vibration amplitude of y = Steady state vibration amplitude of y2 = mm mm e) In your PDF solutions, draw the particular solution (steady state solution) y,p(t) and y2,p(f) as a function of time and annotate your diagrams with the key quantities.