MAT2705-04/05 20F Quiz 8 Print Name (Last, First) _________________________________|__Show all work, including mental steps, in a clearly organized way that speaks for itself. Use proper mathematical notation, identifying expressions by their proper symbols (introducing them if necessary), and use EQUAL SIGNS and arrows when appropriate. Always SIMPLIFY expressions. BOX final short answers. LABEL parts of problem. Keep answers EXACT (but give decimal approximations for interpretation). Indicate where technology is used and what type (Maple, GC).
1. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY5LUkjbW5HRiQ2JVEiMkYnLyUwZm9udF9zdHlsZV9uYW1lR1EpMkR+SW5wdXRGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYuUSJ+RidGL0YyLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y7LyUpc3RyZXRjaHlHRjsvJSpzeW1tZXRyaWNHRjsvJShsYXJnZW9wR0Y7LyUubW92YWJsZWxpbWl0c0dGOy8lJ2FjY2VudEdGOy8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkotSSNtaUdGJDYmUSJ5RicvJSdpdGFsaWNHUSV0cnVlRidGLy9GM1EnaXRhbGljRictRjY2LlEiJ0YnRi9GMkY5RjxGPkZARkJGREZGL0ZJUSwwLjExMTExMTFlbUYnRktGVi1JKG1mZW5jZWRHRiQ2JS1GIzYlLUZONiZRInRGJ0ZRRi9GVEYvRjJGL0YyLUY2Ni5RIitGJ0YvRjJGOUY8Rj5GQEZCRkRGRi9GSVEsMC4yMjIyMjIyZW1GJy9GTEZhby1GLDYlUSMyMEYnRi9GMkY1Rk1GVkZlbkZdby1GLDYlUSUxMzAwRidGL0YyRjVGTUZlbi1GNjYuUSI9RidGL0YyRjlGPEY+RkBGQkZERkYvRklRLDAuMjc3Nzc3OGVtRicvRkxGXXAtRiw2JVEjNTBGJ0YvRjJGNS1GTjYmUSRjb3NGJy9GUkY7Ri9GMi1GZm42JS1GIzYoLUYsNiVRIzI1RidGL0YyRjVGNUZqbkYvRjJGL0YyRjI= , LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JlEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtSSNtbkdGJDYlUSIwRidGMi9GNlEnbm9ybWFsRidGMkZBRjJGQS1JI21vR0YkNi5RIj1GJ0YyRkEvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZXRj1GMkZB, y '(0) = LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW5HRiQ2JVEiMEYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRi9GMg== [Maple notation].
a) State Maple's solution of the initial value problem (use function notation LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtRiw2JlEidEYnRi9GMkY1RjIvRjZRJ25vcm1hbEYnRjJGQC1GLDYjUSFGJ0YyRkA=).b) Put the DE into standard linear form (unit leading coefficient). Then identify the values of the damping constant and characteristic time 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 , the natural frequency LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEnJiM5Njk7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGNC8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2Ji1JI21uR0YkNiVRIjBGJ0Y1RjcvRjNRJXRydWVGJ0Y1L0Y4USdpdGFsaWNGJy8lL3N1YnNjcmlwdHNoaWZ0R0Y/LUYvNiNRIUYnRjVGNw== , and the quality factor LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiUUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTkYyRjw=LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEoJm9tZWdhO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lK2V4ZWN1dGFibGVHRjEvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUklbXJvd0dGJDYlLUkjbW5HRiQ2JVEiMEYnRjJGNEYyRjQvJS9zdWJzY3JpcHRzaGlmdEdGPQ==LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEmJnRhdTtGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJStleGVjdXRhYmxlR0YxLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JJW1yb3dHRiQ2JS1JI21uR0YkNiVRIjBGJ0YyRjRGMkY0LyUvc3Vic2NyaXB0c2hpZnRHRj0=, exactly and numerically. Is this underdamped, critically damped or overdamped?
c) Find the general solution by hand, showing all steps.d) Find the solution satisfying the initial conditions, showing all steps.
e) Give exact and numerical values of the amplitude and phase shift of the steady state solution (the particular solution!) and re-express this sinusoidal function in phase-shifted cosine form. [Make sure you use a diagram to justify your values.] State what numerical fraction of a cycle (LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW5HRiQ2JVEiMkYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LlEifkYnRi9GMi8lJmZlbmNlR0YxLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRjEvJSpzeW1tZXRyaWNHRjEvJShsYXJnZW9wR0YxLyUubW92YWJsZWxpbWl0c0dGMS8lJ2FjY2VudEdGMS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkktSSNtaUdGJDYmUScmIzk2MDtGJy8lJ2l0YWxpY0dGMUYvRjJGL0Yy) the phase shift is (i.e., evaluate LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEnJiM5NDg7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGMkY0/2\317\200) as well as its numerical value in degrees, and whether the cosine curve is shifted left (earlier in time) or right (later in time) on the time line (by a phase less than or equal to half a cycle of course). Explain. [You can check by graphing!]f) Plot the solution and its steady state part together in a window where at the last peak, the pixels of the two curves finally merge so one cannot distinguish the two curves. Make a sketch of what you see, including labeled axes and tickmarks, and label the two curves.
g) Find the two envelope functions of the decaying oscillating transient solution (the homogeneous part of the solution) and in a separate plot without the full solution, plot them together with that transient. Then make a rough hand sketch of what you see for 5 characteristic decay times for the envelope, including labeled axes and tickmarks.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.a) 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5.6:MFNWtKUb<ob<R=MDLCdNNZI[=?[<J:dJvUqoR@QXLCTJcDXoXuuV=sComtw;xYggSCf@yijAC?Oh`?CgMdlATBCGCYfqcifMdcivCgfpUdNoxK_gLUgbofRAGlOspQfcwVdKGiGWNCtbKt^MCK]f?eVNcHMucyay`mrFAVBYiSceiyfIyfYSxuWV`aeuuwswvVYXhySdGgcGC;;Z:nZovu;@;>ZjpH>:gh=B:;hp=:;BPq[:>:Qu;B:;UuB:ltHJ:<rTI:<FB:k<<Ze;;BRJ:^OB:;>>Zj<;Je[:VGB:AfZ=GB?JBXJGeSGeOyEN_dN?LTKTNw]XL<TU<Uu<V:urg\\K;qMDmn?auQyJLanAAY>DtO\\vDuMx@y:@NYtuP]tp<u>\\uDLpMXlfUMKyJ<PweeRjAsI@U<=kbTw@URfQn=tXveOZ=TF\\otArTiYUXxsUr=yQqXyWAtWIMqHtR\\nKiOCAPeqMatmwdXcDv[ET_Ym@]wBdVGdUmTu?pKHXPoevkhqrIXN`pkilGxM_yqJEwO]SnyVvpp``m^HKNpmtENhaw?`k<QotmlNUlFAOvak?yypUU]mQhhlR@UFPoQaSVPm<`SUIsHhQQlPPqTj<pDYnk=m;PT>tl[UV`mOX]W>qUr]lamN_AXoLjZLkMmvUxkYltdqsIhlI<ONQltxSvHUVUXnyQ^<YF=PetW@`WGToYmMxxr;ep]eUQxVLXvHQlctkEqUQYP_uRcPvaTuGyUptWHHnt`oNuwoDljTWAIp^yUo@vgPV@<vA`xH`uUtUJuW@ij>`rQdPjxrceQBdnUMlcpqWLxMxSVEKMMU?au?yXQhlxlpfQUn=WFDtaly^aJaAjZuXEdTFuwvmOvhuIYQfAL>PMpANaLo<dXK\\x@YwD=lREmOHw[quxEp?eKLMXMtVu@QIqtvyqqusM=saMNv@OqeQI]Rr@wDTSc`xLxxDMVklSIas;QtnMvqYvoaP@MpyEyp`wKEsmxNSHW^Ms]lr>hsaQnWhp@<SKdOoIN^HL>DtSEvwXu?tOdqw@ynQXJvTJMPWRylLAMcEkVTLflJgqxsXL[xnl<u`hUaiwuqKOhUrEVUxtxMSGTUQYkWYjgisNHmstL<MRI]J`prV@moHWI=vlIslhqKaRLaoWesOiWHlycMUXHXkPnuAKa]lv\\Sr@LsmQcIxmQO@TY;dj?ikX`Vn@V[QQaIYrEUjDYWQk:Al<poODNiUSlTXEDQLdJt=NSlLo\\W]yOkeVBlTYiQv\\kZ=N=pyHUW=IRMHMKmwUTrDLVqPLx@Li`WkDw?IWpPpr@luDp\\ln@TT^lRl`o<AuY`uHtvo<NlmjX`r=qOVEQOavvhOBEnNdlN\\MIhSl]KlXlieQjIMIPTIuQDeWmqULMX@XmwxleeKnPNraLQlvjaP<@v`@vUYm@aVnhMqXY^mNsyn[<srdTgDsSTLOHwKHPqUWTTODLpmIwohKWhmOyXhxuIEV\\LkHTY\\xXFIT[AKWeWu]xnUrZtTYMX@IJqtw[tVIhOOuwcUlxDnITXlToi]MCDSeAXPEoxxLkYtlip;HpS]xdlJEMK?hrbPsEeknYUstX=]s=qJ><w@`tYDlRaVy@MdPPoEkaXlK<K^xJLHnAij@EnUuPrtropsVIMPxPqHMrtoo]r[Xnrlw:]XxuOx]rtLww`WXXW[XPXmU<]vTUlL\\v?Pmt\\R=@Lt]s_HUH]tmIjAloQ@n=ymShy^IXapuBMkw@xqmQjmxRXphlVZhL[<tBdOy@nsQuFuo]pS]tkQYt;eLqlR?Mj@aruQpUawkDl<UoQHmbepX@VaptCDj^`jkuVoUroTWrmXEXJ@eVHQmoljVdXApja\\toApC`jsqXFQrRhWuXLRdMWQTxEryyvB`Qp`L^hTFhmPqomxm``QfYveamexYVtQGeoh=s]LqgQTZtJUYO<aOWiPf`ylMXvQmy=SC<NXxJK`XMMPfLs_AMTLY;hpplPeePyQVFakgHpaISF]nfawoMkeHjSuOseLIHwqIYh]jKpk>`rkTwLYN<Hsb]JItvZqy]Hn:mKYpQlYj[UN@HkDhwCQObLSwHvrYLR]ubeNgdusmXEawfeKAQsBhj\\Lud]J;]xohptDxhQlO<s>YqvIm]QrYUT>AT\\@lDpkU\\lalm]TX`eXwImMQUuTVdYt`Mw]\\t<\\jS`XsDtGqWsPYqYmB]loXVPpUSiv?]ObAQT]RwPYtTMwXRKINZLuIQkaetNatptRRHw?\\olINQAPMQnCEypYMF<VTpJ@LJPmRdiVhQWGUSG]r@hqdPmPLjjxvZmroYQSyqRhxHaOEesuhrUuMHerE=kkXnYmQCMo[AuaIqmxVCTY]pNexXutQs<lpyPlyKEioHmj\\LUTuWupwaeN`PkJ<MuLUhUxDhUgMu^ps>@O_LOJHuoeXahU]ppyiQo`TAINBLwDTTMuwNxOQuTiqWMpQ]xt]DmG=WrMt_uXLekN`PpXnFEo`AYrlucEkOUSAlSKQWCXLalQXmXqIVk\\st@r:ATJ]XYxpVUrCqKiUylAXS]MqQjKHOBhXoaK;qnWpkXlUlLvR`t^MLGXY_mx=axPpj@EtfUX>iVpDLUhsNdNFEL<dkNluaXxhDpMuNbyplUXLmkAdMD=nmyYxuy;hWRdXnlrHLvkDTAuY>YTqlWr@onPLSIvvdUJuwaytoUqC`jRUq@ynCTyPeOpukBYWNptTEYZ\\VWuVPEQ=mjnhXitjHDM<IyyYxyqqnIrQmWdmnWxUqhYcXrQAj;EO]DjcIRNxRCPXclRcTxhPODUOueVRPpXdLjqPgQUaXRBhoREoSuPThwmpl`lniMQ;uyeLRZHLTdOiHytMkHpK`hlUXXdLx\\MumERlQN]iMuejihQ`]uZlM]QjrpoTPj<@kQiLNLmqmybiv?iuhMtq]x`]NMpYx<rilmHpWotJ>TqUXoNprV@wZqVgHs`LMBERSLREmnNl_Y`^^qZlV[cFsnFd=pqq>oxhiRy`jQv=Py[PsTPqpVopfoqXrEQn?o^SanyvcMH_nPpQakI?mK>gT?wLv`QWenpcBhyToi<ilmvtLNkX_qe`o_gkJNg@>x`Qfp@kLOlLvoWAvNNtZ>a_grkQqpW[QIaEopFpuq>`tViegdgYg>Fwsx_PXyBPrmW^fn^mYt[NmTNsiAl]pc?wn`itxorcIarAyuGudOf>ib@ObsQk]ad@i`JY\\I`ZYVct_yTHr>?`]^lafsTOqvgvLWoHVa;NgLV]eW_Xai>?l[Wn>o\\Zi[>P^>?iO@[xOw^plPppVPmCWbjp[<o[YhjiofHxwZq]di[iYaeXkDPmqhuhO^SntHFrdPeg?hWwvvVeUonMv`U^_lwhr`pW`eGW[mQup^vQisHprT@aFVkkayXiv=Ij[_g]w^_`vjXhoHciqiSocXVhfyjsvqXvmTHwK^lPVwAgny?kowbHHy>pfqncRXpTYjZonG`vX@xGncDgkFYn^gyWfiVakxYma?toQykqx>NjIad]^uYyyGv[FPs\\w`uXylAgfqZ=_[lis=a_wH\\lYwX@iHGmOha[WuPW`wGytPjUGh[GfxW_ifacYo^@xxIxgQ_tfqLa_h@o^wcAhaXw`mypB`cGfkrNf]qtjhma?wsfoTIpMq`sarxXwkYqIX]FAgUhsy>dv@iK_rq_glPjW`yiHsSygtigmHm@Ndng_t^xNid\\xsGY[EPZ\\highl>g`xayhV_@y^^n^m`pXXgKOmjV^na]pfylPuhOpdnh:g\\[NsRX[ag[khcnVwsyiCH\\N_Zk`vcOwUFnrPpnXtqqlPOpOqnOim`N\\\\gwjY_pywiQrgQkPWa\\pkd_jhyaSPc[nyFG^DVeGItMaevhyBnvw`mJHexGy^Iwl^mMInWqk@hnoOeBO]GfcwghHYfDycYQ]xxhsv_mHeEYhgobLqyf_jS?\\wymOwfDO_NG[[wnVynkqaCXyTy^qNp]P_RxsHgeGAho^pdaeIwgvOmsWorxf?iuLQg@oltQvPpmDQoFw^xawUvd<abNpfhguYa_:QmN@]LimD_x\\n_cVfEHkO`nDovEyvHw\\eN`yvx<?rW?p?_rWap=W`w`u<n]RnwtVpUqmsotogs[ocLy\\mifoydWylxWldgfogZYobNN`CWjJFhTimu`ZNWuj?t:WtIIsqFnD`pwWsbAmbNr^pp=g^[>s=f_NvyGygkHkXPZlQ^mNiQxhN_iZQunahYXj;Yc?pwiyg??xKn_x>]xa_c>_bfmavuD`aDfp>foRawEhwOote`iDYrDycwNiIHlMfo`xx?_ZZYsyqaqOyXouh^dqNmBOkiwt_A]Ryrqwwrgdo_yRnZT^uRNkWF`FOqQyhcNsia^_W`OA[PAgTq\\awbSX`:?lCnmAviYo_NGv=yuA>fN`lbFafyyWxgdAawpeHvjZHct`sax_EWas`kvAlKVqgyaChaeXx@QmgAqJNqBgdV`gWgcD?\\;yjMPihXvh^^:OwsY^^nusVc\\xh_xZy`ftx`CIxq@kNacnIxVYlaNkxIqqN[ghr_xrVagHygPxyt?hyxy^Pu\\nrBhpSW_V?j:@_HImawqiF^HHjJQrv@ktN^v`ifpa[Adjvijgkofhyiuq`t;yagpjlxue>ecamihr:XajHisImvYwQGaQ?cs>kJxhQaocFtmQmZowdQxs@dIW\\=pp?xaeIuavdVg`dFhm^mM>_HothpjLNvxh[oa[JFqCX[BVoP>mcYnoqh?F_aok?audvc_NiJOtwV^]^e`fxTQ\\_P`uqhX`lvQkc>gp^`ywvUVoiqp]hvkpb<oqqpZ[wsHpdsQnohpOfewYqlop;FmpHZ=`oUatVaalxj]OwRQbtibrP]r_xbIxLQdO`cpXixVs=qu^Y]N`cqFviG\\[wnHXbHqgmQaR_n]YhJxhfaZXaf[HivGc@Ym[OiHWqyp]Vy]RFo\\wvTWunPpIOqrIoBNl@phP@ilOtTW\\;_yo?yBgkkVf@g_pqeyfo?AvL_pWXaqwgTFmC`tJpxW`pnf]bA_rfxkohmQl;gkj_yypwGidNfkoxkhfwTA\\LhrfWm_HkLAbI?kvNhtFlpQ];AfjVnxxphQw`vqhFvi`]<^kAHr_gwRwhya[^AmtfbUvyyNZfYmwqgof`gVbeHaQgypNyaftN>\\w@krquUQy;qcVO]R>_uFZWyyQ^]SGft@u;vuX_y<wuKqpoqtVfmXxrWospib<fk>Fa\\^lbhivXl=^[QPuq@\\LPw\\xuMfcyqoYNk`a]:Awda`nQjuhsEAo^A^IXwrVywFdXQj]w^jYkHneS_^xw]t?sqOjSYbEWffWwkO_iV`<xh?aqoA^IFpm@vqI\\A@rEq[\\nuIVnsng<vprQo`nacVrMard?^GimJO_bnhtpoJGrZ`k<pmKa`g^^EpfTqhMqo`fZgf\\@_gxg^XghNql[gaawc^oieV\\mwxYpxmPj]O`>Aj;NiTXgWi[L_]dQ]Zg_w^qfYe?@mkNmpqeXnlRou\\@pQQhDh\\oi_fggGHayWkYh\\ufuRApo?r>xyT@kdOdHo]PvnyY[_gswWiNoexYwvv_@hn]OgRQqZ^\\=XdPW]>nnh_o@pcawggIiGhlZ@_CFfp^`jvjlp]KXr]ps_OtU^rt`l=XdS^s=WiFwbexa`foFpu_x`^ony^sW>[??[P^hvQhJF\\AolxoylibNqnWgeD?]T>xj`xRqwBIsMYfI_fUiafFlTNxX@pNPq;A`jIx]_pufiivo=_h]HsZYppgspfrNai`@o?wk\\hoGh`yGdRYykNk`Y^e^t`FgcppqQ]HaiDWwM>^Dyw^PhIgZ:QmUF]wWqCFm<vsrhyWX[CyjY_pvih>o\\wvhCnyPF\\HQxaxyro_JQyVolO@\\S^qsgvVidAxgQAki`k@O_dhh]hdaPskA]?y_evZ:G\\v?y_A^BNni?nMQtfhiroyfIoNAmpfeyPx`F[wF^ehjO^vXnmCA^Ywqw>_Fi]y`\\vYwd@gXapiqbMpq]?j\\FmGidRV^^_biob]?iovvwXm_gr?xmR__<AnCNvQfgIqgLN`pW`Ggvu@axXitIn?Awc>c<PiKG\\<^wtasannLHdWVn?XblHaw`xcYctWuF`^tYsahsL?tTVt=a_SnyPbo?euOwYmTRwYscG^aegysf=GDgxs;gW?uOQe=oyLOgxyxMGDXIrDwey?hRYfpgycmvuGFGQX]CyfuINOUxIEa]wp]xjUumye?kvhGvwuyeKRjqfGYUPKf\\]IlmXuUXfQuoqBAIgBstQWXxMf[CWqQhSmxm=HLoIU=WFgVUqWHyh^gdw?DKgfqQffGI>EfmkT]WuGmBWgh]AUvmXyMgi]gMCeJestQrG]U?qCWKteqgCsY]mggGRM;igcW]]esyti;xFgEiURxocpUwhEiNorFGUtcEHiRYKdqUugAiTYhAKIZeSq]Ur[FhCeAObtEtXkxIExP_cKaVE[WVCEoORYmiB?s\\ov>UhroDdwfKeW[wrvAxpOb^]CBkueQdQubkwFqmVLmWh=dWKUBITxuytYvTcFWUucOw\\QFO]cXoyn]F;WH\\MSYeXNWff;hRsXioEGeGAuIVSvXIv]udgocgcWiycFoTJmwqeRB[HlAxXUxV[ulUthWBrKlHAo==P\\llgiMEyRreOSTvvpybETIQTdeLQeMeYmV`SOIs@QQBmPghq_iKExoYdM]IsdhuhMPbaoWpw>IwR]NCHk^HlMTsgYuXdYWulKhrG\\NnqyMmqREqNaspaKT@vopp\\xsIQqKmrWERtlsXhjd`ohqXNxlyiYaXRqlVo]yAdvFuT@dJHAw[eyMPwNqQhIKbQjlXleLRO\\PvpsSqjKDYLXLQPwvasQMo`pJDPleDMFaOMIqRMPtTsLymy`V[dov@LPYsaaXXQuAaXPlnuQr>]jq@k>XjZuYQeQaIUDdrK`UqUNgAti`R@DN\\YWPqoydndPWdEPWDs@uQweRgeWU@MDtQsHUkmpKUp?AynIx]tyI@v^avTYW;@MHePJxwieRBluM=w>ApHus:MJadR^=RcXp?xwTYXphwSdydxjoqXMLydIuB@YMTWWLNGdy\\xsJulthlq@xniNi`X<urTaJYYj`TjGQuCYur\\OsLlNtT=@T]lxYhtIdUpDKEywL@w=QvItJmmmKDjm=muTTX]jMxuMtRWxmdiO\\eO;yYghWDiNOPXGxVfawaMXHIUitS^tn[<QaxYHuyd=Y<mRuympPuB@M=QOwHLOdY_txGAMmhnEqTTxkuQuQLtOIP<INn]TydwrmvGetCIRhpY^xpmxxVuKnhM[DpLHrREQhHtZtRjhtHEYJhsTXt\\aXwmTpYJhQXFUVGXVEat;qODTLKLu\\LLhiXnQPTtWwuQsYYHmmudyhMPGDtRAVpiXAUnydndFhOQsMHufIhFAsFYntOmBvnaqtOfa`qmnP^gGwkY^YItRPx=HaP`l>@v@Yms@iugpD>tlpmQPxHqf;IafVmapuiQkbWaI^xXGZswnq`fjN_@n\\dNvuAvQ^q]Q[UXvx_gyfjXhlYobJigKVucVsIQvf^ajp`e^]kiadOtQ_iq>dMGkCQgiwZnab[nbpIjoYkVy[YXsf>isQx_YpuIkkVqWwliavNPhcFafahqP\\hQgcFZMAafpk[xhuywlYdwhb^>ejyeMF\\MFfvXo`qejo]cAuNgi]ab>fdTQhEFrF_kmhdT_ryYuYi[BykXQqmN`[V_iV_X@w_qbvXstQwuQmfFhUHrs?kQov?Ys?`sPxi]HjHp]FnqwQdwpma?yHq[Ggm>>c@Arow^;Wlw@p\\_mI^[DoohO\\ppv;`mf`d_hbXXsFNi`^c^@ySGZ=?oeGxJodRfsUpgsvrgV`iaewYk@hpnge^ngmA^y_]Qhm`nrx^gZIklHkgNn=ybRY\\VNi:>f:xkJYddfvg_myigZfs>QoTnyjFc;?^ropHNoiW\\IxeAWiM`dUHjYyaD@vy_l\\Fbs>[uGZ\\ntEftXokhah\\?dBYusGyHqbAwaoAky_kJAwao\\@AyYFbqPi^h[VaeUo_]OqKafjGyp?[aAvj@hyysXHbCxoxfd_ar@VpyI[XWlLpdSxp=@q]xxE`drIoXQ^DWb?voC@cs``o`e\\`hcnkw>tRvwX`uyvhxwt[YwLq[uai>Ax[WpOHwKH`qGqs_iiWkL@yChf^AjOwwm_xrH`kfbMvloq\\<vqpPqd`kygemgxhowPVlihdjVoifxYyy\\y^YxqDX[BpeUqawawvVeIG]sgyfqihOb\\IaDGfwnbwopa?mqXsnfbCxlFNjk^hyY^nY^ticCqihxwD_ax_mgxjgVcBp[wflKWsgQnXioI`ybQpjFe?ycsWuBYtoix>fqHoi`ay?Occandqn\\ahDfbeqgv?vYgx@VmPYk]YrGHy]AqZ^sGqa]okEQrSVrdPdCyfLWkTBcegOSYICYp_QZlRQivR=qnyouDkeao]lNSHuRNa?WfRYwaFmc_fDY^@VcDOcconA?rHqpwwnii\\KWbCHkvhk`Hjpnlao^mYfLx]ip]qIyNpsga]]vnwAqKQeWF]V_vMPjhHhWNw@QkV`x`ywGWahivX_gdpsgV^T@`ywbEhbPPnwqMGXUwtiad<KfUWweweVyvUOGmSX]YR<MvE?ULMX@WwI[womW]ifoUfC_vSUIckSBIhWAg]kRMqI:_HoEsoWxKwDLwEysg<uSXWr\\qReMwTuGWuwnsu:eB]KxGCdHkujWDFsTJEdPOYm[srUvLoH;mYSebk[iQaeg]vUqg[eI=yxjsx@_F`mBMKH_etauyU]EaYXNwx_uhC]F;qC<_dVOfTAS^iW?eW=cIG_tv=D]Ow\\ix<eGFoVgKTtOXcobuoe]]DvSG@]SxOYnSg\\GuPWtkqfQSVHuUCaIqYu@AS`KGwchCSdg[UvqHGqHQCy:KWC]dFsyUOUYUFYGSB]iL[icKd;aRy?ggwvPsf?WHo=XgUibud?Gu:gdQAdMOgTKWvoXgaE[Ast_i?wXrqEsWbaCsNAxY]YjMYEKBHeWXwF`oW@sXVssAUY=MYTIt:YWbAGX_VoouhyRACt]?U@AVsIRLGYxKIhYthcVMOWU;tAwdyuImedcggg?W[ox=OFdywWUIDMShEIIAfeEdtQrnKT[sWoKxwWSAMTZat?khugXakgIiieoY>MFWEDlQH^yReCsp[TQEHXuv`KdreDIWCFwXnOITAB]Win[dnYRdIyEwdhmV?UyX]I:OGJUXlWxiogE_WUYEuiubMtQkBCkERqBZcci;gSycewuJUVpqUVKvSsDeQbACd:?H;EDWMbOODZmw=mV\\kdxIG;qxvitleuOuWesyn[BeAhyqdYgDv[H_=bsqC>=BZKH]eCg[WgeT^WgTudECBZ[SJ]RaaIVeEwSVnABbOcygbIOt_qyniWYsR;ktH;Du;IOchtQuT=HfCRR?fBog]OiZEc]kC[aVXKxyurGII>IIHyhKwBO=boWB>aBPcHS_S=]Cgeso?RP;FF=T>uXvWImKrHuB_CGdIDyAGnSIoGg[IVNwyK_IncrN]gMuhyGF@ObB<wL<yfDxnEMHIrwmmt<s<\\jCLkbqMDpTxEpKmJa<ky]WltKi=RJDUoIMEQJ\\qPFYt@xr;@joXJ>ajT`mj@njQJSTqwhoDam:<L`<O\\Xk@tSYIXu]j]qXJtqrLJK`SZYJgTNk`V\\DVYqns<xJlOJlNbLJR\\o:eJ<<J:<J:lqW<:;joXJ:<J:<Jj>Z:>Z:BeuJ:>Z:hp=B:<JR?:;B:TWA<J:<J:<f;>Z:BRJ:^OB:;>>Zj<;Je[:>RJ:\\oW<J:>Z:Gyy?qIxuu`o<WjB@Z:B:MTKWDKWgJ;eZ5:\"\{\}-%+ANNOTATIONG6'-%)BOUNDS_XG6#,$-%&FloatG6#%)infinityG!""-%)BOUNDS_YGF'-%-BOUNDS_WIDTHGF'-%.BOUNDS_HEIGHTGF'-%)CHILDRENG6"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The first two terms which decay are the transient, the last two terms which simply oscillate are the steady state solution.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b) Divide through the equation by the leading coefficient to read off the two physical parameters.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEkZGVxRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjNRJ25vcm1hbEYnThe solution frequency of 25 is just a bit below the natural frequency 25.5.This system is generously underdamped, comparing: 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c) check out the homogeneous solution.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The general homogeneous solution is a linear combination of the real and imaginary parts of this complex exponential.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 method of undetermined coefficients determines the particular solution. We pass on that here. Check out the hand solution.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d) The steady state solution coefficient vector is in the first quadrant near 90 degrees, so the cosine peak is pushed just less than an 1/4th of a cycle to the right. 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phase shift: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compare phase, shifted right by just less than 1/4 cycle, measuring time in units of phase instead of time units (multiply by the frequency)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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=f)
The envelope functions 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Compared to the driving funciton rescaled to have the same amplitude as the steady state solution.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