Consider a permanent magnet dc $\text{(PMDC)}$ motor which is initially at rest. At $t=0$, a dc voltage of $5 V$ is applied to the motor. Its speed monotonically increase from $0 \text{ rad/s}$ to $6.32 \text{ rad/s}$ in $0.5 \: s$ and finally settles to $10 \text{ rad/s}$. Assuming that the armature inductance of the motor is negligible, the transfer function for the motor is
- $\dfrac{10}{0.5s+1} \\$
- $\dfrac{2}{0.5s+1} \\$
- $\dfrac{2}{s+0.5} \\$
- $\dfrac{10}{s+0.5}$