midterm2.pdf

# Ancl u0 1 r o ia find the iisplacement u ns a

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ancl u,{0) : 1. r ----o ' ia) Find the iisplacement u ns a functjon of timc. r-i i.ri t i i'.i !. i,.,_ti '. .t r i,- I. t L, ll ,I ,t ./\ '-'i "1 r"^-;: t{" { i-' -' l- i' (b) lvhat is the .raximum dispracement of the svstcm. li ..'l .; "_ i. t' . t" {:.' ; { il I I '- ii .,{ I L', i ,, .! , t i\ i.. i ii i-", .{., i i- - t"l !-t i;.\ li 1 t," " i i i a, ,, ,.{ rtl ii ii., l "\ \ '"rtgrl rr*Ni {4..1 s ii i \ I ..::' '" :

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2. tL\ pts) A mass weighing 8 lb strctchcs a spri-ng l" ft and it is attached to a dashpot *rechanism that has a Aaniping constant of 2 lb.s/ft. The nrass is set in motion from its equilibrium position with an initial downward velocity of 6 ft/s, and is moreover acted on by an exiernal force of 20 cos 8t lb. (Assume the gravitational acccleration is 3? ttlsz). (a) Formulatc the initial value problem describing the motion of the mass. *, {"Ya :: :.{iS : ,'*";d"4 {t^ " {i ! ltr: rJ dJ, J--- ., \ ttf'"r- l{ ", '*'*i ..,\L., * x ii."ir,, - '*:* ' L \it l "l r"ii-=\ J'r 1... r j '.,*- -'(b) 1y16, 1ig' f .irx-*."*r i **-*^-Je,*,* I { ; I * qf,for..,::o& *" L.{. "l l*'*tq{'P:} fi.,1;,t: u, L ,- It fu'*t'r# i {-*""*"* [ -r. {" -X e, - r 1 1 n{ii + ?.-*{ "t"X i",1. = '*-.*, ig.,:;'* ! LLiu\;: t1 LL t{";1 Find the solution to the above initial relue problem' - ) ('r. r + :Jc .a".\ *, ff ::) nu,, ':* * 1...--L".,*-.":_]__* .: T """L -J".. 3 4&{f { 1 :" *:-t+ k, Ltu: i-r" i -f il'"u !,u*,1 q { } t- , t i' - nc'. J,lt-.b. i;.-,1 * tr**'1'.. , i'i tr .- 4L i.{i* -!* t 'f iL 'nrt:'* {' " o{"u} * -t el',i..\ t t t rtl' i-t'l':*** d' t'{*i i* --{rl &,;q$uL -"tt$r:,rtr"x "iLfl lr .,1- i Ll il L.; .i l{ h l,*,: \& -6 \}\ {iii1 L t' * ? fi'rn'l: '{ :: ? {i i.,t::.'5' { .'. t \$." 1 -tr-v. t- -*. "x q: *r* li 'f- _ % fl,, * i{.t .- I q:, ] **, " tq ft.. {} L"" i { i {conti,nued nert Page) "- ) l flt ., *f*-\ -"" / 1- L I I -;"*-'* *_**__l d- ' r il'
t*; i t i =, -"it tcu" "'b't "- *.t'{* i \{:rx*t*"rt :*-*L* l-tair", .' *r*.

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• Fall '08
• NAGY,KRISZTINA
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