Laplace Transform of Typical Function Sinusoidal Function f(t)=0 fort<0 F(S)=? f(t)=Asin ot for t≥0 f(t)=0 for t<0 and t>to Impulse Function ()=lim for0 F(S)=? i0→0t0 6(t-to)=0fort≠to δ(t-to)=∞fort=to F(s)=? Unit Impulse Function [6(t-to)dt =1 Table A.1,by OgataLaplace Transform of Typical Function Impulse Function Unit Impulse Function             0 0 0 0 ( ) lim for 0 ( ) 0 for 0 and t t 0 t t t A f t f t t t                    ( ) 1 ( ) for t t ( ) 0 for t 0 0 0 0 0 t t dt t t t t t    F s() ?  F s() ?         ( ) sin for 0 ( ) 0 for 0 f t A t t f t t  Sinusoidal Function F s() ?  Table A.1, by Ogata