7.5 Exercises 149 tion 7.1 I) with thc Laplace transform completel) in the frequriicydomain (Sectioris 7.1.4 7.2, 7.3.1, 7.3.2) system itrialysis with the Lnplacc traiisforrn in the freyIier~c.y-clorrr;i~iarid calciilatiori of the iriterrd pail in tEir tirrir-tlomain (Sccl ion 7.3 ) The classical solution is cei tairily the most camplic-atecl nic.thoc1 in terriis of cakuIittion cdfoit as it works cxclubively in the time-clorusin It i\ difficult to guess a par6ictrlar soliitioii for higher-order svstenis If the Laplace transforiii is nsed t o articular solulioii, thr classiral solution tiirns into the$ third proccd~~ie ly in tlw f i rquoncy11 :i~inlysis with t he Liiplacrl !ransforrrr coriipl the inost s i i i t n M e procwlurc i t the internal cttue of the systc’m ih known, for cxaunple, an clecshic*alor prcseiitntioii Then tbr iii\ t i l k 01 ! , h ~iiiitial vdLi(’S ierndl part c m be d&wziiined cithci tr The transfcx 1unc.tion G (s) aird i m t i i c ~ ~ s :ire obtained directly tiorrr t h e te-spmxb representation Cnlritlatiort of tlic Intcmal p a r t in the time-domain i s witable if t1w iiitc~iial structure is unknown, and orilj the difI‘tJreiitia1cqiiation arid the jnitial coiiditiorrs have beer1 givrn ‘Tlir II stiry calculation steps are simple t o carry oiit if the miinei ical values of the tliffvrcrrtridrquatiorr coc4kicirts have bcm provided ises