典型常見(jiàn)函數(shù)拉氏變換表

1、.1典型常見(jiàn)函數(shù)典型常見(jiàn)函數(shù)拉氏變換表拉氏變換表.2序號(hào)序號(hào)原函數(shù)原函數(shù) f(t) (t 0)象函數(shù)象函數(shù) F(s)=Lf(t)11 (單位階躍函數(shù)單位階躍函數(shù))1s2 (t) (單位脈沖函數(shù)單位脈沖函數(shù))13K (常數(shù)常數(shù))Ks4t (單位斜坡函數(shù)單位斜坡函數(shù))1s2典型常見(jiàn)函數(shù)拉氏變換表典型常見(jiàn)函數(shù)拉氏變換表.3序號(hào)序號(hào)原函數(shù)原函數(shù) f(t) (t 0)象函數(shù)象函數(shù) F(s) = Lf(t)5t n (n=1, 2, )n!s n+16e -at1s + a7tn e -at (n=1, 2, )n!(s+a) n+18 1 T1Ts + 1tTe典型常見(jiàn)時(shí)間函數(shù)拉氏變換表典型常見(jiàn)時(shí)間函數(shù)

2、拉氏變換表.4典型時(shí)間函數(shù)的拉普拉斯變換典型時(shí)間函數(shù)的拉普拉斯變換序號(hào)序號(hào)原函數(shù)原函數(shù) f(t) (t 0)象函數(shù)象函數(shù) F(s) = Lf(t)9sin t s2+ 210cos tss2+ 211e -at sin t (s+a)2+ 212e -at cos ts+a(s+a)2+ 2.5典型時(shí)間函數(shù)的拉普拉斯變換典型時(shí)間函數(shù)的拉普拉斯變換序號(hào)序號(hào)原函數(shù)原函數(shù) f(t) (t 0)象函數(shù)象函數(shù) F(s) = Lf(t)13 (1- -e -at )1s(s+a)14 (e -at - -e -bt )1(s+a) (s+b)15 (b be -bt - -ae at )s(s+a) (s

3、+b)16sin( t + ) cos + s sin s2+ 21a1b- -a1b- -a.6典型時(shí)間函數(shù)的拉普拉斯變換典型時(shí)間函數(shù)的拉普拉斯變換序號(hào)序號(hào)原函數(shù)原函數(shù) f(t) (t 0)象函數(shù)象函數(shù) F(s) = Lf(t)17 e -nt sin n 1- - 2 t n2s2+2ns+ n218 e -nt sin n 1- - 2 t1s2+2ns+ n219 e -nt sin( n 1- - 2 t - - )ss2+2ns+ n2 = arctan n1- - 21 n 1- - 211- - 21- - 2 .7典型時(shí)間函數(shù)的拉普拉斯變換典型時(shí)間函數(shù)的拉普拉斯變換序號(hào)序號(hào)原

4、函數(shù)原函數(shù) f(t) (t 0)象函數(shù)象函數(shù) F(s) = Lf(t)20 1- - e -nt sin( n 1- - 2 t + + ) n2s(s2+2ns+ n2) = arctan211- -cos t 2s(s2+ 2)22 t - - sin t 2s(s2+ 2)23 t sin t2 s(s2+ 2)211- - 21- - 2 .8)0()0()()(222fSfsFSdttfdL( )( )(0)dLf tSF sfdt)(lim)(lim)0(0ssFtffst)(lim)(lim0ssFtfst f(t) g(t)L= F s G s)0()0()()(222fSfsFSdttf