14.2 拉普拉斯变换的基本性质 1.线性性质 若[f()]=F(s),出[f()】=F2(s) 则[A)+A,f)]=A,[f)]+A,2[f2()] =A,F(S)+A2F2(S)A1,A为任意实常数 证:2[A0+A,)=[A0+AO A(te"d+(te"de =A F(s)+A2F2(S)14.2 拉普拉斯变换的基本性质 1.线性性质 f t f t e dt st 0 1 1 2 2 A ( ) A ( ) f t e dt f t e dt st st 0 2 2 0 1 1 A ( ) A ( ) A ( ) A ( ) 1 1 2 2 F s F s A ( ) A ( ) 1 1 2 2 F s F s [ ( )] ( ) , [ ( )] ( ) 1 1 2 2 若 f t F s f t F s A ( ) A ( ) 1 1 2 2 则 f t f t A ( ) A ( ) 1 1 2 2 f t f t A ( ) A ( ) 1 1 2 2 证: f t f t A1 , A2 为任意实常数