Question

A-kg mass is attached to a spring with stiffness 40 N/m. The damping constant for the system is 2 N-sec/m. If 15 the mass is moved 8 - m to the left of equilibrium and given an initial leftward velocity of į 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.

Answer 1

Mas Sel Given V4 Stiffness & YON/m dlampige constant - 2 N-secm Moved 15/8 m left leftware initial velocity 3/2 m/sec. To finals ① Eg" of motion of mass damping freston Queri period 16 duasifrequency. ① According to question, .. we need to selves 4 " + 2y + 40 y = 0 y + 8 y + 16oy 2 M= So, general Consider the characteristic equation? G +84 +160 =) = -85 64-649 $ -4I lai sol" is in Tu (t) = = e "t (c, cos (1241+ (2 sin (124) Griven initial condition, ing g (o)= (-5) = e(c, cose + casino) GE so -15/8 -1.875 C 0.79.17 2 =-25 13.6+ 134+ 5 = Y* (-11875 608 (26) +(-0.7017) sin (ast)) y ) CS Scanned with CamScanner

- 4+ clearly damping facter is he Quasiperiod 2TT 2 T 12 I sit B 6 Hence A B 6 Slicesi freguesery of Au CS Scanned with CamScanner

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