● Submit your work to Gradescope The quiz is open-book and open-notes. You may use the Canvas course site, but no other online resources. Collaboration is not allowed - this is a solo effort! Please show all work Lasers can be used to drill the hip socket for the insertion of an artificial hip joint. The use of lasers for surgery requires high accuracy for position and velocity response. Consider the system shown in the block diagram below, which uses a DC manipulator for the laser. We select a motor with a field time constant T₁ = 0.1 s and a motor-plus-load time constant T₂ = 0.2 s. Motor & manipulator R(s) ► a. Asymptotes (if any) b. C. Amplifier K 1 S(T₁S + 1)(T₂S + 1) ►Y(s) Figure 1. Control system for laser surgery. Sketch the Root Locus by hand (do not use MATLAB). Find and show the following points of interest on the sketch (you must provide hand calculations for credit): Break-away/break-in points (if any) Imaginary axis crossings (if any) and the range of amplifier gain K that yields a stable system

Fig: 1