A electromechanical relay for a plant automation equipment behaves like a pure delay of \(\tau\) seconds, for which the transfer function is \(G_{relay}(s) = e^{-\tau s}\). For \(s = j\omega\) where \(\omega\) is a non-negative real number, please find:
1) \(|G_{relay}(j\omega)|\) and \(\angle G_{relay}(j\omega)\) (10 points)
2) For \(\omega = 0\), please give the value/limit of \(|G_{relay}(j\omega)|\) and \(\angle G_{relay}(j\omega)\) (8 points)
3) For \(\omega \to \infty\), please give the value/limit of \(|G_{relay}(j\omega)|\) and \(\angle G_{relay}(j\omega)\) (8 points)
