文檔lc無阻尼受迫(交流)振蕩電路-全文預(yù)覽
【正文】 φ)根據(jù)定理二，微分方程LC*d2i/dt2+i=EmCωcos(ωt+φ)的一個(gè)特解為：i=EmCω/(1LCω2)*cos(ωt+φ)則根據(jù)定理一，方程LC*d2i/dt2+i=EmCωcos(ωt+φ)通解為：i=Asin[(1/LC)1/2t]+Bcos[(1/LC)1/2t]+EmCω/(1LCω2)*cos(ωt+φ)當(dāng)t=0時(shí)，因電感上電流不突變，所以i=0，代入上式，得0=Asin0+Bcos0+EmCω/(1LCω2)*cosφ0=B+EmCω/(1LCω2)*cosφB=EmCω/(LCω21)*cosφ代回原式，得i=Asin[(1/LC)1/2t]+EmCω/(LCω21)*cosφcos[(1/LC)1/2t]+EmCω/(1LCω2)*cos(ωt+φ)兩側(cè)求導(dǎo)，得di/dt=A(1/LC)1/2cos[(1/LC)1/2t]EmCω(1/LC)1/2/(LCω21)*cosφsin[(1/LC)1/2t]EmCω2/(1LCω2)*sin(ωt+φ)當(dāng)t=0時(shí)，因電容上電壓不突變，所以uC=0，則uL=L*di/dt=e=Emsin(ωt+φ)=Emsinφ，所以di/dt=Emsinφ/L代入上式，得Emsinφ/L=A(1/LC)1/2cos0EmCω(1/LC)1/2/(LCω21)*cosφsin0EmCω2/(1LCω2)*sinφEmsinφ/L=A(1/LC)1/2EmCω2/(1LCω2)*sinφA(1/LC)1/2=Emsinφ/L+EmCω2/(1LCω2)*sinφA(1/LC)1/2=Emsinφ[1/L+Cω2/(1LCω2)]A(1/LC)1/2=Emsinφ[(1LCω2)/(LL2Cω2)+LCω2/(LL2Cω2)]A(1/LC)1/2=Emsinφ[1/(LL2Cω2)]A=Emsinφ/(LL2Cω2)*(LC)1/2A=Em(C/L)1/2sinφ/(1LCω2)代回原式，得i=Em(C/L)1/2sinφ/(1LCω2)sin[(1/LC)1/2t]+EmCω/(LCω21)*cosφcos[(1/LC)1/2t]+EmCω/(1LCω2)*cos(ωt+φ)i=Em/(1LCω2)*{(C/L)1/2sinφsin[(1/LC)1/2t]Cωcosφ
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