Question

如图所示电路，求其系统函数，并写出微分方程

Answer 1

(1/L)∫[e(t)-r(t)]dt+C0=r(t)/R+Cdr(t)/dt
[e(t)-r(t)]/2=r'(t)/2+r''(t)/4
r''(t)+2r'(t)+2r(t)=4e(t)

追问

能否给个过程啊

追答

流过电感的电流是电阻和电容上的电流之和
电感的电流是il(t),电压=e(t)-r(t)=Ldil(t)/dt,所以il(t)=(1/L)∫[e(t)-r(t)]dt+C0
电容的电流ic(t)=Cdr(t)/dt
所以(1/L)∫[e(t)-r(t)]dt+C0=r(t)/R+Cdr(t)/dt
两边求导则[e(t)-r(t)]/L=r'(t)/R+Cr''(t)
整理得e(t)=r(t)+Lr'(t)/R+LCr''(t)
代入得e(t)=r(t)+r'(t)+r''(t)/2，r''(t)+2r'(t)+2r(t)=2e(t)
我那个还搞错了耶！