The TF from U to Y is  . If the input u(t) = 4 sin (2t), what will be the particular solution y(t) in time-domain? 

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 objectiveFind the TF from U to Y1.  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 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’ll get some partial credit for that.    Auto-graded questions (2 points) If you draw the FBD of the pendulum, how many forces will be shown in it? [three] (6points) Equation for the electrical side:V = [R]I + [Kb]ω T = [Kt]*I(6points) Equation for the mechanical side.You’ll have to use the small angle approximation: 

After a systems analyst documents the system’s requirements, they break the system down into subsystems and modules in a process called ___________

Cartons of product are supposed to weigh exactly 32 grams. Inspectors want to develop process control charts. Employees weigh seven boxes five times each shift (the mean and range of each sample is given). Based on the following data, compute the 3σ upper control limit for the range. Report answer to 2 decimal places. Sample Mean Range 1 {a} {t} 2 {b} {u} 3 {c} {v} 4 {d} {w} 5 {e} {x}

Identify the four costs of quality and illustrate each cost by applying to a restaurant/fast food type of business.

Cartons of product are supposed to weigh exactly 64 grams. Inspectors want to develop process control charts. Employees weigh eight boxes seven times each day (the mean and range of each sample is given). Based on the following data, compute the 3σ lower control limit for the mean. Report answer to 2 decimal places. Sample Mean Range 1 {a} {t} 2 {b} {u} 3 {c} {v} 4 {d} {w} 5 {e} {x} 6 {f} {y} 7 {g} {z}

Based on the data below, use the exponential smoothing method with a smoothing constant of {c} to find the forecast of 2025? (enter your answer to the nearest tenth, i.e., report one decimal point) Data: 2023 actual demand: {x} and forecast {xx} 2024 actual demand: {y} 2025 forecast?

A company is deciding if it should design a product in-house or outsource the design.  To design in-house would require overtime for an already stretched design team with total costs of ${ic}.  If outsourced, it is unknown what type of bidder will respond.  The bids will be either low or high.  If a low cost bidder is found,  the cost is estimated to be ${lb}.  The estimated cost from an expensive bidder would be ${hb}.  All three designs (in-house, low bid, high bid) are equal in quality and the likelihood of finding a low bidder is {p}%. What is the expected cost of the outsourced design? (enter your answer to the nearest whole number and only enter digits – i.e., do not enter the “$”)

Which type of control chart should be used to monitor the number of defective electronic components in a batch of 200 units?

Why can the use of a Pareto Chart make large improvements in quality?