Q$1.$ A rotating load is connected to a field$-$controlled DC motor with negligible field inductance. A test results in the output load reaching a speed of $2(1-\frac{1}{e})$~~$2**63\%ra\frac{d}{sec}$ within $\frac{1}{2}sec$ when a constant input of $100$ V is applied to the motor terminals. The output steady$-$state speed from the same test is found to be $2ra\frac{d}{sec}.$ Determine $K$ and $$ in the transfer function $\frac{(s)}{V_f(s)}=\frac{K}{s+1}$ of the motor.

Requirement: Please do not apply the inverse Laplace transform to find the step response.