Correct Answer - Option 2 : 20
Concept:
Time constant \(\tau = \frac{{ - 1}}{{{\rm{real\ part\ of\ Dominant\ pole}}}}\)
Calculation:
\(40\frac{{dx}}{{dt}} + 2x = f\left( t \right)\)
Taking Laplace transform, we get
40 s X(s) + 2X(s) = 12(s)
\(\frac{{X\left( s \right)}}{{F\left( s \right)}} = \frac{1}{{40s + 2}}\)
\( = \frac{1}{{40\left( {s + \frac{1}{{20}}} \right)}}\)
Pole will be at -1/20.
Time constant \( = \frac{1}{{pole}} = 20\)