Question

描绘系统的微分方程为y''(t)+2y'(t)+y(t)=x'(t)+2x(t),试求其冲激响应

Answer 1

y0''(t)+2y0'(t)+y0(t)=δ(t)
laplace变换
p^2Y(p)+2pY(p)+Y(p)=1
Y(p)=1/(p+1)^2
反laplace变换有
y0(t)=t*exp(-t)*u(t)
y(t)=y0'(t)+2y0(t)=exp(-t)*u(t)*(t+1)