Control Systems Engineering Exam Reference Manual (ULTIMATE | PACK)

| ( f(t) ) for ( t \ge 0 ) | ( F(s) ) | ROC | |------------------------------|------------|-----| | ( \delta(t) ) | 1 | All ( s ) | | ( u(t) ) | ( \frac1s ) | ( \textRe(s) > 0 ) | | ( t ) | ( \frac1s^2 ) | ( \textRe(s) > 0 ) | | ( e^-at ) | ( \frac1s+a ) | ( \textRe(s) > -a ) | | ( \sin(\omega t) ) | ( \frac\omegas^2 + \omega^2 ) | ( \textRe(s) > 0 ) | | ( \cos(\omega t) ) | ( \fracss^2 + \omega^2 ) | ( \textRe(s) > 0 ) | | ( e^-at \sin(\omega t) ) | ( \frac\omega(s+a)^2 + \omega^2 ) | ( \textRe(s) > -a ) | | ( t e^-at ) | ( \frac1(s+a)^2 ) | ( \textRe(s) > -a ) |