Question

A 4-kg mass is attached to a spring with stiffness 112 N/m. The damping constant for the system is 16/7 N-sec/m. If the mass is pulled 20 cm to the right of equilibrium and given an initial rightward velocity of 2 m/sec, what is the maximum displacement from equilibrium that it will attain? 1 -2/7 617 1 (2+.4/7) 67 2+ meters. The maximum displacement is e (Type an exact answer, using radicals as needed.)

Answer 1

det alt denotes number metres to Yhe Hight equbirni that The ma is tseconds Naw, yl Seluhon to IVP my"lt by ) ky hure m- k 12., ylo)=A= 0, y'lo-0-3 , b= /6J To solu, the DE, the charactevistic equahon is o 91+zh releatd Toots Xニ -2JF, -9 Jet r= J7 rebeatad T0ots Henu, x -T Saluin ho DE is. -at yiGettet CGCt)et Castonts Na, Using inihal conditins Jlo)= Co) A lo, t ara ot e 2--t) et B-(Ar+8)xt) pasitrue Nou, 'lt= Since, (ArB) y'lto y'ti y'to ane if t At)r it t- R Y

By fiyst donivahie test, ylt o,) at has global maximum on (Art8)Y And valu o lt) at t (ArB) is Y Crtstlet A+ (Art3) B CArB)Y e TArBr 용) e Art (A+ B Now Substituhig we get yman 3t02.2J7 Mar e -I89 0578 e O 0873 m 8.13Cm