Question

A 1/3 kg mass is attached to a spring with stiffness 54 N/m...

A5-kg mass is attached to a spring with stiffness 54 N/m. The damping constant for the system is 6 N-sec/m. If the mass is movedm to the left of equilibrium and given an initial leftward velocity of 7 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) = (Type an exact answer, using radicals as needed.) The damping factor is The quasiperiod is seconds The quasifrequency is Hz.

I need help please!

Answer 1

y(t) = 138" +by+ 54y = 0 Hoots of characterstic equation are, 75 g + 6y' + suy=0 y" + 18y' + 162y = 0 = -9 798 so general solution is, ylt) = é at 16, Cos (at) + C Sin 19t)) Solving IVP, 1. yio) = -22 . y'(0) = -2 -2 ylt) = €9+ (-5, Sincat). (9.) + scos (at).9 ) >> Gr.6=7 os y(t) = 29t13 cos (9+) + sin ( +)) Damping factor is Le-98 Since, 3*+12=(Vio)? :: 941 a o entiende coslov + ste sin (941) . - vic eft 1 Cos (9+-)) where, .d = tan' (173)

Quasi period = 21 им ,и Чmk - м 2м S - - чx 4х54 -1ку- 2х) 6 . Quasi period = 27 = 1 quasi frequency v . and пCA