math 383 test 2 solutions

math 383 test 2 solutions - Text" 2 S's/whats Math 533...

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Unformatted text preview: Text" 2. S's/whats Math 533 5‘ Pk) Problem 1. Consider the differential equation my”+ky’+cy=Fsin(wt) _.. Q (a) Find the particular solution of this problem. If 5?: A Stkwi? + Emsw‘t _ . K ‘ ‘91P": +Auoowi7 - Fav’gmwt W”: “$3? $0 0 beam» ,MUALHP +C—Jk-i-K5P’: Cg-Mw’) (ALb‘iwt-fBaJui-J . . +l< (Awasat— Busflwt) ‘ :L‘. -<A(G‘MWL)+M '~ BK“) ) Svkwl" + (B (C‘MWL) +Akw) “5‘4“.“ . :=' \Fsmwtfl ' Ami??? (b) Under what conditions on m, k and c do we have real, distinct roots for the characteristic equation ? KLalmw )0 I l ( c) Under what conditions do we have resonance in this problem ? Raow bum-5 MW 69' sea) as ch“ PJ‘UEVBM‘ o r 5-) Problem 3. Find the general solution to the problems : (a) 16 Y”(X) + 24 Y’(X) f 9 Y(X)- — 0 . "Id—5:9 .39 \6}.+2.q.)+?=o ____/_.___ ‘52- T )3 "i2: = ”if; (M44321 mt) ‘ 10 W) (b) y +=2y+5y Sinxcosx. I N )1. , ‘ «f .. M o .I .. .. Jaguar“ Mm fill/LET?“ (4,,»th (Ln-La 12.3.;ka5-5 $42,; = 2.9:“; aux, w. WHITE Hg; SAL an. 2 947mg; ' . 2... =3 5,: Asdzz + 64052:; /’"/’( RX fix .5p :2 A-S'WI 21L +8605 9-?- , jp’: 1490327; “Rafi Stilt— \ 3‘," : "LfASMlK “‘ LE5 CM 9.9. , \\ _. ll , __ sun. 9 5‘4—23 +59... 2—1_ SW 4 . . I ‘ 3(1): t. (clash. +¢,_ sum + J- Smlsc. "‘13: 00529:. 3’1‘ 14 ...
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