Question

u(t) represents the unit step function. The Laplace transform of u(t - τ) is
1. \(\frac{1}{{s\tau }}\)
2. \(\frac{1}{{s - \tau }}\)
3. \(\frac{{{e^{ - s\tau }}}}{s}\)
4. e^-sτ

Answer 1

Correct Answer - Option 3 : \(\frac{{{e^{ - s\tau }}}}{s}\)

\(\begin{array}{l} u\left( t \right) \leftrightarrow \frac{1}{s}\\ f\left( t \right) = u\left( {t - \tau } \right) \end{array}\) 

\(\begin{array}{l} L\left[ {f\left( t \right)} \right] = L\left[ {u\left( {t - \tau } \right)} \right]\\ = {e^{ - s\tau \;}}L\left[ {u\left( t \right)} \right] = \frac{{{e^{ - s\tau }}}}{s} \end{array}\)