精品課件大學(xué)物理2(雙語)(參考版)
2025-04-22 15:54本頁面
【正文】 求全響應(yīng)其中：設(shè)例)(,)()(,),()(11tytekthjstetfnitisti???????????0)(1?? ??tectynitixi 解： ???????nitistf tektethtftyi1)()()()()( ?? ??????nitstii teeski1)(][ ???? ?? ???????ninitstiitifxii eeskectytyty1 1][)()()(??? 全響應(yīng)stni iitni iii eskeskci ???? ?????11][???固有響應(yīng) 強制響應(yīng) 。 ttf ??? )(39。)()()(:??????????tftftftftftftftfe x a m p l eCT convolution Differentiation and Integration of convolution convolution properties ?? )()(.1 ttf ? )(tf??? )()( 0tttf ? )( 0ttf ?)()()( 2121 tttfttttf ?????? ? shifting if f1(t) ? f2(t) = y(t) then f1(t ? t1) ? f2(t ? t2) = y(t ? t1 ? t2) )()( 2211 ttfttfSo l ut i on ???：??? dttftf )()( 2211 ???? ? ???dxxtttfxfxt)()( 21211???? ? ??????)( 21 ttty ????????dfttfttfttft)()()()()()()(.4 )1()1(? ??????????)()(.3 39。( )()(39。 ,),0(),0(),0(zeroinput solution零輸入響應(yīng) linear differential equations solution 2. zerostate solution 注：兩種解法的區(qū)別，初始條件代入的先后次序不同 3. total solution Homogeneous solution (zeroinput solution) n階齊次方程的解（零輸入響應(yīng)的求解） 0)()(0)()( 0111 ???????? ?? tyapapaptypD xnnn1. The roots of the characteristic polynomial 求特征方程的根 2. Homogeneous solution 根據(jù)特征根得值，寫出零輸入響應(yīng) ????????nititnttxiin ecececectyt h e nr o o t sd i s t i c tna r eIf1212121)( , ??????? ，①The roots of the characteristic polynomial are called natural frequencies. These are frequencies for which there is an output in the absence of an input. )(, 21 tyccc xn 代入，得零輸入響應(yīng)將 ?例： 47頁 ， 50頁 tjtjx ecectyjr o o t sc o m p l e x)(2)(12,1)( ????????? ?????、?????? ??????nijtjritirixrjecetctyr o o t stn o n d i s t i n c11211)( ?????②The unit impulse response and zerostate response of system Unit impulse response The unit impulse response gives intuition about the properties of a system. The impulse response is the response of a system to unit impulse signal. 系統(tǒng))( t? )( th零狀態(tài)Relationship of H(p) amp。 (3)若初始條件發(fā)生變化，則須全部重求解。 (t)+8y(t) = f(t)一個特解 yp(t) (forced solution強制響應(yīng) ) yp(t)=(1/11)sint+(?2/33)cost c. Now we need to find a particular solution to the differential equation 0,c o s33211s i n66126653)( 42 ????? ?? ttteety ttzeroinput solution零輸入響應(yīng) linear differential equations solution )()()( tytyty ph ??由上例的求解過程，可看出經(jīng)典法有如下的不足之處： (1)若微分方程右邊激勵項較復(fù)雜，則難以處理。39。 (t)+6y39。(0)=2, f(t) = sin t u(t) y39。(t)+6y39。 Example: y39。)( 00 tfdttttf ????????4???Examples Calculate the integrations Differentiation and Integration )()0( tpfDtDD? D2D? 2)()( D?DDtpf)()( D?D?Dtpf0?????DD D??
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