Question

4.9.9 3 Question Help A 4-kg mass is attached to a spring with stiffness 108 N/m. The damping constant for the system is 2413 N-sec/m. If the mass is pulled 20 cm to the right of equilibrium and given an initial rightward velocity of 3 m/sec, what is the maximum displacement from equilibrium that it will attain? The maximum displacement is meters. (Type an exact answer, using radicals as needed.) Enter your answer in the answer box and then click Check Answer. All parts showing Clear All Check Answer

Answer 1

we have m=urg k= 108 N/m (=2463 Nosechm XO) = 20 m = oogm Too X'(o)= 3 m/s

The differential equation is mx" + cx' + x = 0 4x" +41.5692193816531 x' +108 x = 0 auxilary equation is 4^2 +41.5692193816531 r + 108 = 0 root r=-5.196 hence solution is x(t) = (c1+c2*t) e^(-5.196 t) c1 = 0.2 -5.196 cl + c2 = 3 On solving, we get C1 = 0.2 c2 =4.0392 Hence x(t) = (0.2 +4.0392 t)e^(-5.196 t) maximum displacemnt = 0.143 meters answer