Exercises 5.5The frst equation yieldsz=−x+1k(mD2+2k)2[x]=1k2(mD2k)2−1[x],(5.30)and so−(mD2k)[x]+(mD2k)±1k2(mD2k)2−1[x]²=(mD2k)1k2(mD2k)2−2[x]=0.The characteristic equation For this homogeneous linear equation with constant coeﬃcients is(mr2k)1k2(mr2k)2−2=0,which splits onto two equations,mr2k⇒r=±ir2km(5.31)and1k2(mr2k)2−2=0⇒(mr2k)2−2k2⇒³mr2k−√2k´³mr2k+√2k´⇒r=±is(2−√2)km,r=±is(2 +√2)km.(5.32)Solutions (5.31) and (5.32) give normal Frequencesω1=12πr2km,ω2=12πs(2−√2)km3=1
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This note was uploaded on 03/29/2010 for the course MATH 54257 taught by Professor Hald,oh during the Spring '10 term at University of California, Berkeley.