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

  1. $\frac{10}{0.5s+1}$
  2. $\frac{2}{0.5s+1}$
  3. $\frac{2}{s+0.5}$
  4. $\frac{10}{s+0.5}$
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