For the system model shown in the figure, assume k, = k = kg = k...

  

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For the system model shown in the figure, assume k, = k₂ = kg = k = (Z + 1) × 100 and m₁ = m₂ = m3 = m = (2+1), where Z is the last digit of your PMU ID. a) Derive the three equations of motion in terms of k and m. b) Find the mass and stiffness matrices, [m] and [K] and state the equation relating those two matrices with the eigenvalue 2. c) Given the modal vectors as stated below, plot the corresponding mode shapes by scale. (Z+1) (Z+1) 2 and -2 000 m₂ F₁(0) 000 M₂ F(0) 000 my F,(1) For the system model shown in the figure, assume k, = k₂ = kg = k = (Z + 1) × 100 and m₁ = m₂ = m3 = m = (2+1), where Z is the last digit of your PMU ID. a) Derive the three equations of motion in terms of k and m. b) Find the mass and stiffness matrices, [m] and [K] and state the equation relating those two matrices with the eigenvalue 2. c) Given the modal vectors as stated below, plot the corresponding mode shapes by scale. (Z+1) (Z+1) 2 and -2 000 m₂ F₁(0) 000 M₂ F(0) 000 my F,(1)