拉氏逆变换F(p)=p/(p+1)平方+16F(P)=p/p平方-p-6

Question

拉氏逆变换
F(p)=p/(p+1)平方+16
F(P)=p/p平方-p-6

Answer 1

1,F(p)=(p+1-1)/[(p+1)^2+16]=(p+1)/[(p+1)^2+16]-(1/4)*4/[(p+1)^2+16],所以其逆变换为
e^(-t)cos4t-(1/4)e^(-t)sin4t
2,F(p)=p/(p-3)(p+2)=(1/5)*[3/(p-3)+2(p+2)],所以逆变换为[3e^(3t)+2e^(-2t)]/5