第二章1信号与系统,课后答案

第二章21已知描述系统的微分方程和初始状态如下，试求其零输入相应（1）YT5YT6YTFT,Y01,Y01解微分方程对应的特征方程为2560其特征根为12，23,系统的零输入响应可写为YZITC1E2TC2E3T又0Y01,1,则有1123由以上两式联立，解得21即系统的零输入响应为T2,T2微分方程的特征方程为其特征根系统的零输入响应可写为又2,则有以上两式联立，解得因此系统的零输入响应为，3微分方程对应的特征方程为其特征根为1，系统的零输入响应可写为又则有，1以上两式联立，解得因此系统的零输入响应为,4微分方程对应的特征方程为其特征根为系统的零输入响应可写为又则有0因此系统的零输入响应为5微分方程对应的特征方程为其特征根为,系统的零输入响应可写为又则有以上三式联立，解得，因此系统的零输入响应为,T22已知描述系统的微分方程和初始态度如下，试求其1输入则方程右端不含冲激函数项，则FT及其导数在T0处均不发生跃变，即2将代入微分方程，有1由于方程右端含有项，则，设T2其中不含及其导数项。对式两边从到T积分，得2TB3其中T，而T故不含及其导数项。同理，对式两边从到T积分，得34其中及其导数项。将式代入式，整理得2341AT8A6BC比较上式两端及其各阶导数前的系数，有A16AB08A6BC0以上三式联立，解得A1,B6,C28对两式两端从积分，得23B6则有（3）将代入微分方程，有1由于方程右端含有项，则中含有，设TC2其中不含及其导数项。对式两端从到T积分，得2TB3其中T,不含及其导数项。对式两端从到T积分，得34其中B，不含及其导数项。将式代入中，整理得2341T3A4BC比较上式两端及其导数前的系数，有A14AB03A4BC1以上三式联立，解得A1,B4,C14对两断从积分，得23则有42,FT由FT求得将上式代入微分方程，得1由于方程右端含项，则中含，设2其中不含及其导数项。对式两端从到T积分，得2T3其中AT，不含及其导数项将与上式代入式，整理得231A45T2比较上式两端前系数，知A1对式两端从积分，得23A1因此，23如图所示RC电路中，已知R1，C05F，电容的初始状态1V，试求激励电压源为下列函数时电容电压的全响应T1234解根据电路列出微分方程，有RC代入元件参数值，整理得1当时，系统的微分方程为由于方程右端不含冲激项，故微分方程的齐次解为易求其特解为故微分方程的完全解为代入初始值故因此，电路在的激励作用下的全响应为2当时，系统的微分方程为由于方程右端不含冲激项，故微分方程的齐次解为易求其特解为故微分方程的完全解为代入初始值，有因此电路在时全响应为3当时，系统的微分方程为由于方程右端不含冲激项，故微分方程的齐次解为易求其特解为故微分方程的完全解为代入初始值，有因此电路在时全响应为（4）当时，系统的微分方程为由于方程右端不含冲激项，故微分方程的齐次解为易求其特解为故微分方程的完全解为代入初始值，有因此电路在时全响应为24已知描述系统的微分方程和初始状态如下，试求其零输入响应，零状态响应和全响应。（1）2,解（1）由零输入响应的定义，可知（英文版）EASILYBLAME,TOPREVENTTHEBROKENWINDOWEFFECTSUPERVISETHELEADINGCADRESTOPLAYANEXEMPLARYROLE,TAKETHELEADINTHESTRICTIMPLEMENTATIONOFTHEAND,LEADTOSAFEGUARDTHESOLEMNITYANDAUTHORITYOFTHEPARTYDISCIPLINE,ENSURETHATTHEPARTYDISCIPLINEANDTHELAWSANDREGULATIONSFORIMPLEMENTATIONINPLACETHROUGHOUTTHEDISCIPLINEINTHEDAILYSUPERVISIONANDMANAGEMENT,STRENGTHENSUPERVISIONANDINSPECTION,FROMTHETHOROUGHINVESTIGATIONOFVIOLATIONSOFDISCIPLINEBEHAVIORSTRENGTHENTOKEYAREAS,KEYDEPARTMENTSANDKEYPROJECTSASWELLASTHEMASSESREFLECTTHECONCENTRATIONOFTHEUNITSANDDEPARTMENTSFORSUPERVISIONSTRENGTHENINGSUPERVISION,DISCIPLINEINSPECTIONANDSUPERVISIONOFCADRESTOSETANEXAMPLEFORCOMPLIANCEWITHTHEANDISAMANMUSTBEHEXYL,BLACKSMITHNEEDSITSOWNHARDWAREDISCIPLINEINSPECTIONORGANSASTHEEXECUTOROFTHEPARTYDISCIPLINE,ANDSUPERVISOROFTHEDEFENDERS,FORITSSUPERVISIONMUSTBEMORESTRICTLY,DISCIPLINEINSPECTIONANDSUPERVISIONOFCADRESTOFIRMLYESTABLISHTHEAWARENESSOFPARTYCONSTITUTION,SENSEOFDISCIPLINEANDRULESCONSCIOUSNESS,POLITICSLOYALTY,SENSEOBEYACTIONSPEAKJIORDINANCETOSETANEXAMPLEOFTHEREGULATIONSOFTHERULEOFLAW,STRENGTHENSUPERVISIONANDACCEPTTHESUPERVISIONOFTHEFIRMNESSANDCONSCIOUSNESS,DOCOMPLYWITHANDTOFIRMLYESTABLISHTHEDISCIPLINEMUSTFIRSTBEDISCIPLINED,THESUPERVISORWILLBESUBJECTTOTHESUPERVISIONOF“CONCEPT,ANDCONSCIOUSLYSAFEGUARDANDIMPLEMENTPARTYCOMPASSESPARTY,TAKETHELEADINPRACTICING“THREESTRICTREALSTRICT,SOLOYAL,CLEAN,PLAYTOBEGOODATLEARNING,THECONSTITUTIONANDTHEASMORALITY,POLITICSANDBROUGHTTOFRUITIONTOIMPLEMENT,DONOTWANTTO,DARENOT,NOTWITHDISCIPLINARYRULERTOSUPERVISIONTODISCIPLINEARULER,OFTENTHECONTROLINSPECTION,ANDCONSCIOUSLYINTHEIDEOLOGICALREDLINETODRAWTHEROWMINGGOODACCUMULATIONISINDEEDTHEBOTTOMLINE,SOTHATTHEHEARTHASFEAR,SAIDTOHAVEQUIT,THELINEHASENDEDATTACHEDINDIFFERENTTOHEART,CALMLYTOTHETABLEINOURLIFE,THEREAREMANYUNPREDICTABLETHINGSWILLHAPPEN,SOMEGOOD,SOMEBADTHINGS,WECANNOTCONTROLISPOWERLESSTOSTOP,BUTWITHTIME,YOUWILLFINDINLIFESOMETIMESTURNSOUTTOBENOTGOOD,SOMEBADTHINGSFINALLYTURNEDOUTTOBEAGOODTHING,BUTTHENWEMUDDYHOWEVERDIDNOTKNOW,THISISTHELIFETEACHUSTHINGS1,LIFECANBECOMPLEX,CANALSOBESIMPLEWANTSIMPLELIFEOFPRECIPITATION,TOHAVEENOUGHTIMETOREFLECT,TOMAKEBECOMEMOREPERFECTLIFEISTHEMOSTIMPORTANTTHINGISNOTTOWIN,BUTTHESTRUGGLENOTTOHAVECONQUERED,BUTTOHAVEFOUGHTWELL2,THEPLAINISTHEBACKGROUNDOFLIFELIVEAPLAINLIFE,GIVEUPONTHEMSELVESISNOTACOWARD,BUTTHEWISEANSWERSNOTDISILLUSIONEDAFTERTHEHEART,SUCHASASHES,BUTEXPERIENCETHESTORMAFTERTHEENLIGHTENMENTNOTUNREWARDINGPERFUNCTORILY,BUTCALMATTITUDEOFLIFEOFUNRESTRAINEDSELFCONFIDENCEPLAINLIVING,THEREISNONOISENOISY,NOEARTHLYTROUBLES,MOREDIDNOTFILLINTHEDISCONTENTOFDESIRE,SOMEJUSTACALM,ACALM3,MEMORYOFHEARTWILLNOTGOODTHINGSTOERASETHE,LIFEISAWHENNOMOVIE,PAINISABEGINNING,THESTRUGGLEISAKINDOFPROCESS,DEATHISAKINDOFENDINGGIVEUPTHISGIVINGUPISTHEHELPLESS,DONOTGIVEUPTHEABANDONED,DONOTGIVEUPTHISGIVINGUPISIGNORANCE,DONOTGIVEUPSHOULDNOTGIVEUPISPERSISTENT4,ATHINGFIGUREDISHEAVEN,THINKIMPASSABILITYISHELLSINCETHELIVING,TOLIVEBETTERSOMETIMESWEBECAUSEOFTOONARROWMINDED,TOOCAREAROUNDTHECHORESANDPENNYWISEANDPOUNDFOOLISH,NOTWORTHTHECANDLESOMETHINGSTOATTRACTTROUBLEANDWORRY,COMPLETELYDEPENDSONHOWWELOOKATANDDEALWITHITDONTALWAYSTAKEEVERYTHINGBACKTOTHINGS,ANDDONTGETINTOABLINDALLEY,DONTWANTTOFACE,DONTBENARROWMINDEDPOKETOCARE,ISAKINDOFOPENMINDED,AFREEANDEASY5,IAMNOTAFRAIDOFOTHERSBEHINDMEAKNIFE,IAFRAIDTOLOOKBACKANDSEESTABME,ISMYINTENTIONTOTREATPEOPLEIAMNOTAFRAIDOFTHETRUTHTOTELLTHEBESTFRIEND,IMAFRAIDHETURNEDTOITASAJOKETOTELLDONT6,WHENWEAREINAPOSITIVEFRAMEOFMIND,YOUWILLFINDMANYGOODTHINGSANDWHENWEAREINANEGATIVESTATEOFMIND,YOUWILLFINDMANYDEPRESSEDTHINGSLIFEHAPPYANDWORRY,ALLISYOUOFLIFEATTITUDE,OPTIMISTIC,GOODLUCKLOSSOFSINK,ERITREACOMPANYWHENYOUAREINADVERSITY,MAYWISHTOCHANGEAPOINTOFVIEWTOTHINKEVERYTHINGOVERTOTHEGOODTHINK,BECA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