Hoote Law and Differential Equations Questions

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A 10-lb weight is attached to a spring suspended from the ceiling. When the weight comes to rest, the spring is stretched by 1.5 inches.The damping constant for the system is 5*sqrt(2) lbs/(ft/sec). The weight is pulled down 3 inches from the equilibrium position and released.

a) determine the motion of the weight.

b) Determine the damped amplitude, damped natural frequency, and damped period of the subsequent motion.

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natural frequency, and damped period of the Subsequent motion. ma 2 3100 - 10 lb 32 ft/sec - 5 16 Ib-sec² ft is slug a) d=o K = w AL lolb 80 lb ь 24 = 80 1.5 ft ft X 11 mx X + Kx = 0 5 16 aloo } x + 80x = 0 & Co) 3 ft = 4 ft x'(o)=0 ft/sec 5 16 x"+80x=0 x 256x=0 D² +256 = 0 D = = 16 i x (t)=C, Cos(16t) + C₂ sin (16t) x'(t) = -16c, sin (16t) + 16 Cz Cos (16t) x(0) = / 4 = cito C = x'(o)=o=0+16c2 > C2 = 0 = 44 Cos (16t) x X(t)
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