Question

differential equation

01 /8 points l Previous Answers 11 5.1.005 stretches a spring 6 inches. The mass is initially released from rest from a point 9 inches below the equilibrium position 2 s. (Use g 32 ft/s' for the acceleration due to gravity.) (a) Find the position x of the mass at the times t π/12, m/8, π/6, π/4, and 9m/3 x(n/12) x(T/8) ft ft x(T/4) x(9m/32)- (b) What is the velocity of the mass when t3/16 s? ft ft/s In which direction is the mass heading at this instant? downward O upward (c) At what times does the mass pass through the equilibrium position? Need Help? Submit Answer Save Progress Practice Another Version 1 points Z DHEOMOdAD11 5 1006 A force of 480 newtons stretches a spring 2 meters. A mass of 60 kilograms is attached to the end of the spring and is Initially released from the equiibrium position with

Answer 1

To solve this problem our approach will be as follows;

l Solution ven mass weighing 2o poun ds streaches aspring sinches The mass is intially Teleased from rest from a point ginches below the equilitbrium. 리 Obfeun the position x of the moss at the time,t nside the equation of mass-sping system Here damping fosce mass-weight"-924 tis) too (abs]、 -15 - mass-uo eight 8 Deiving fo ce, F(t) Spring constant k 2o (lbs) Sabstitute these values in eguction orde…-E The auxillaey eguatlanaf this homogenous 오 CS anned wit CamScanner

2. 2. 2. m-=-64순 The γ00t's (me complex conjugde ofthe form ㅅ-10 . Thesefor e, the genesal soluion rs, s (t) gos(t) C sin(&t) Given inhal condition, the mass is tiallt released from. Test om a point ginches be lo the equiliba 12 Applyinq initial condiion 4 (i) with γespeof fot. Dif ferentiading both sides ofeqh nt the values of Gs ce in,ef

r(TT/4): ¡cos (8.TF) -오 cosçaTT) ニ4(,) ニo.15 4(-4) _ _ @gges) = o.I+ 44g 32 b) Velocity of the mass ime s x't):-오.ssıns( 8 t) -Ecosで8t) sint The velocity (te) at t: s, rs s'(冊: .csǐの(8.形ニ-6Sin(포) :-6(. 1): c -6C-1 'The.velocity is positive sothed the mass heading 따 th'.s instant is doneds c) The mass pass through the equilibm positin ) cosct) - The mass Passes through the equilibrium position atk浯 (ent).hal