Question

An object weighing 16 lb streches a spring 3 in. The object is attached to a viscous damper with a damping constant of 2 lb-s/ft. If the object is set in motion from its equilibrium position by pulling it downward an additional 1 inch, find the position of the object at any time t.

Answer 1

weight of the spring wang = 16 lb 27 m2 16 lb 16 g Į No.5/ft. 32 ft/s constant be - 2 lb.slft. spring ng 16 lb 3 in L The deputation 16 0.25 lb lft = 64 lb/fil The egn of motion is m da ot² a 2 + kazo dt dia d42 dt + 64920 dx. +4 da dt² dt +2 da 2 E + 128 1zo let nt az e 2 z> n+un+ 12 8 zO

n2 -4 $116 - - 512 2 - 4 I 483) 2 2-2 + 31131 62+21 755) 2(1) Ae (-2-2231) + Be da da A(-2+21131) -24 21 137) + -12-21 Got (-2-25) 8 e + At tzo, X- linch = ft 7 A+B z 12 At tzo, TE 1 -2.621731) - 8(4913- 0 -2 (A+B) +2 i viA-3) 20 A-B2 - 12. from 0 & 2 we reget. 2A> 놈 12 12/31 i Az 24 24 V

8 2 t 24 2 ੫੩) 2iBit -- , + : et ( 2 ) ੬) ਉਥ ‘) 216 - 2 Gil { $ 1 ) 24 vਓ। [ ਕੀ 3 00Sਓ ਤਾ ਵੀ) [ ਇਸਖੇ – ਫ਼ੈਜ਼ L ) -34 alt) z e