Problem $6\mathrm{.}35$

$($a$)$ Obtain the transfer function $\frac{s}{T_L}(s)$ for the field$-$controlled motor of Example $6\mathrm{.}4\mathrm{.}2.$

$($b$)$ Modify the field$-$controlled motor model in Example $6\mathrm{.}4\mathrm{.}2$ so that the output is the angular displacement $,$ rather than the speed $,$ where $={}^{}.$ Obtain the transfer functions $\frac{s}{V_f}(s)$ and $\frac{s}{T_L}(s).$

from Example $6\mathrm{.}4\mathrm{.}2$

Figure $6\mathrm{.}4\mathrm{.}6$ An op$-$amp integrator.