Your boss would like to know the gain and phase of the above sensor for an excitation frequency of 4 radians per second. Knowing that multiplying a signal in the Laplace domain by the Laplace variable, s, is analogous to differentiating the signal, you realize that the sensor’s dynamics in the above problem are equivalent to thefollowing differential equation: dy/dt + y(t) = 0.1u(t)1
Begin by assuming that y(t) = Asin(4t), for some unknown constant, A. Solve for dy/dt and use dt' the above differential equation to solve for u(t).
2. Sketch a phasor diagram that allows you to determine the magnitude and phase of u(t) relative to y(t).
3. Determine the gain of this sensor at the above excitation frequency, in Volts per Celsius, defined as the magnitude of y(t) divided by the magnitude of u(t).
4. Determine the phase of this sensor at the above excitation frequency, in either radians or degrees (please indicate which), defined as the phase of y(t) relative to u(t).

Ashielded metal arc-welding operation is accomplished in a work cell by a fitter and a welder. the fitter takes 5.5 min to load components into the welding fixture at the beginning of the work cycle, and 1.5 min to unload the completed weldment at the end of the cycle. the total ength of the weld seams 1200 mm, and the travel speed used by the welder averages 300 mm/min. every 600 mm of seam length, the welding stick must be changed, which takes 0.8 min. while the fitter is working, the welder is idle (resting): and while the welder is working the fitter is idle. (a) determine the average arc-on time as a fraction of the work cycle time. (b) how much improvement in arc-on time would result if the welder used flux-cored arc welding (manually operated), given that the spool of weld wire must be changed every 10 weldments, and it takes the welder 5.0 min to accomplish the change? (c) what are the production rates for these two cases (weldments completed per hour)? attach your work and solutions.