Congratulations, you have a summer internship with a medical equipment firm. You

Question

Congratulations, you have a summer internship with a medical equipment firm. Your first assignment is to help design the mechanical lift that will move patients into position within a CAT scan system. Some of the main aims of the position control system in a lift are: To bring the patient to the correct height, To minimize travel time, To maximize patient comfort by providing a smooth ride, To accelerate, decelerate, and travel within safe speed limits. Assume for comfort a maximum acceleration of 0.8 m/s/s Two of your colleagues have suggested functions for the "flight path" where the vertical position s(t) (inches) with respect to time t (seconds) for 0

Explanation / Answer

given

s1(t) = -0.00009t^4 + 0.0094t^3 -0.3703t^2 + 6.3723t

s2(t) = 0.00008t^4 - 0.0078t^3 + 0.2167t^2 - 0.2741t

now differentiating the functions

s1'(t) = -0.00036t^3 + 0.0282t^2 -0.7406t + 6.3723

s2'(t) = 0.00024t^3 - 0.0234t^2 + 0.4334t - 0.2741

now differential gives velocity

and the second differential gives accelration

s1''(t) = -0.00108t^2 + 0.0564t -0.7406

s2''(t) = 0.00072t^2 - 0.0468t + 0.4334

at t= 40 maximum accelration is given by

s1''(40) = -0.00108(40)^2 + 0.0564(40) -0.7406 = - 0.2162

s2''(40) = 0.00072(40)^2 - 0.0468(40) + 0.4334 = -0.2866

as shown the accelration of the second flight function is high which also indicates the better slopes and also in the range of maximum accelration so the better flight function is s2(t)

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