Question

8 Až kg mass is attached to a spring with stiffness 16 N/m. The damping constant for the system is 2 N-sec/m. If the mass is moved 15 m to the left of equilibrium and 56 given an initial leftward velocity of 15 m/sec, determine the equation of motion of the mass and give its damping factor, quasiperiod, and quasifrequency. What is the equation of motion? y(t) = 1 (Type an exact answer, using radicals as needed.)

Answer 1

ma 15 Solution Given šky , K = 10 N/m Darsing const) - 2 Neseem mass is mored = 8 (to to the left) Us - 56 m/sec (to the left) Calculate the rear of motion D 3 (0) - and v(u) = x'(o) = 256 con of motion is mx' + cx' + Kx=0 sie x+22'*162 = 0 => m+ 16m +128- >> tom' + 2m +16 20 -16576_ 4x1x128 . 16+ -165 > m= 2 2 نا we get 2 m=a8785 Therefore the solution is X(t) = est Cc, cosst &ęsinst Apply initial condition .x (o)= - 8 3 (0) - ° [c, cos o + sino? 15 C, -8