Long question 2 (Total 20 points) Tests the Core outcomes 1 and 2 A building is modelled as a box of mass m1. It is connected to the ground (L shaped and brown) via a spring k1 and damper c1. During an earthquake, the ground shakes horizontally such that its position is given by u(t) from a fixed reference. The variable y1 is the displacement of the building m1 relative to the ground.  To ‘reduce’ the building motion, a vibration absorber is placed inside the building. It is a mass m2 connected to building via spring k2 and damper c2. The variable y2 is the displacement of m2 relative to the ground (not relative to the building) Your ultimate objectiveWrite all the equations and process to find the TF from U to Y1.   no need to actually find it. Only worry about the motion in the x-direction (which is unaffected by gravity).All friction between the contacting surfaces is modelled via dampers. There is no extra/other/dry friction.Assume all the displacements are measured from the equilibrium positions, Hence, you don’t need the natural lengths of the springs.      Procedure  Work neatly on paper showing all FBDs, all equations, algebra, etc.Neat + clean + organized  = extra credit! Then show your papers to camera, Then complete the auto-graded questions below.  After exam, submit your work as a pdf on canvas.  You may get some partial credit if it applies.    Auto-graded questions  (1 points) Tensile force by spring k1 is:     Fs1 = k1*()(1 points) Tensile force by spring k2 is:     Fs2 = k2*()(2 points) Tensile force by damper c1 is:   Fd1 = c1*()(2 points) Tensile force by damper c2 is:  Fd2 = c2*()(2 points) Acceleration of mass m1 is:   a1 = ()(2 points) Acceleration of mass m2 is:   a2 = () (3 points) Newton’s law for mass1:  (Fs1 + Fd1) (Fs2 +Fd2) = (3 points) Newton’s law for mass2:  (Fs1 + Fd1) (Fs2 +Fd2) = (3 points) To solve for transfer function from U to Y1, you will solve for from Newton’s law for mass 1 and plug it into Newton’s law for mass2. Then you’ll rearrange that resulting equation so that it’s of the form = something*. This something is your transfer function from U to Y1.     

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