Response of Exponential Functions For a physical system described by the transfer function G(s),when the input signal [assumed to be slow compared to the dynamics of G(s)]is in the form (t)=e",then the output signal (under zero initial conditions)will also be exponential. y(t)=g()u(t-t)dr=g(r)edr=g(r)e-dr.e" =G(s)e Convolution Integral Theorem:L[()g(-)d]=F(s)G(s)Response of Exponential Functions • For a physical system described by the transfer function G(s), when the input signal [assumed to be slow compared to the dynamics of G(s)] is in the form , then the output signal (under zero initial conditions) will also be exponential. u ( t )  e s1 t 1 11 1 ( ) 0 00 1 () ( ) ( ) ( ) ( ) ( ) s t s st s t y t g ut d g e d g ede Gs e                    Convolution Integral Theorem: [ ( ) ( ) ] ( ) ( ) 0 L f g t d F s G s t      