A first order system initially at rest has for a signal u(t), the response 1 - e^-t. If the signal is 2u(t) cost, the response will be

A. $$\sqrt 2 \cos \left( {t - \frac{\pi }{4}} \right) - {e^{ - t}}$$

B. $$\sqrt 2 \cos \left( {t - \frac{\pi }{4}} \right) - \frac{1}{2}{e^{ - t}}$$

C. $$2\left( {1 - {e^{ - t}}} \right) + \frac{1}{{\sqrt 2 }}\cos \left( {t - \frac{\pi }{4}} \right)$$

D. $$\sqrt 2 \cos \left( {t\frac{\pi }{4}} \right)$$

Answer: Option A