The motor and load shown in Figure P5.46(a) are used as part of the unity feedback system shown in Figure P5.46(b). Find the value of the coefficient of viscous damping, DL, that must be used in order to yield a closed-loop transient response having a 20% overshoot.

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K, = 2 N-m/A K = 2 V-s/rad J.= 2 kg-m? D.= 2 N-m-s/rad Ra = 22 10 Di JL = 800 kg-m? (a) Motor R(s) + E(s) Gear 1000 & load train (b) FIGURE P5.46 Position control: a. motor and load; b. block diagram