Question

A mass weighing 10 lb stretches a spring 11 in. The mass is attached to a viscous damper with damping constant 3 lb ·s/ft. The mass is pushed upward, contracting the spring a distance of 4 in, and then set into motion with a downward velocity of 2 in/s. Determine the position u of the mass at any time t. Use 32 ft/s as the acceleration due to gravity. Pay close attention to the units. u(t) =

Answer 1

Wzmg 210 ms 20 32 ft sa 11.575 073 lb.5/ft. kamg, hoe 130 lolift The equation of motion is med et begyndet ku 20 a o 90 x 20 scopo Bos Puzo. 11 let, uzeht añ+ 9.6 U + 384 zo 8

ne –9.6 V 19.63* – 4 x 384 ? -9.6 6.99 i 2 . 2 -4.81 3.451 1. So, (- 4.8+3.445 3 t A - (+418+3.45 i) + ult) z +Be 64843.461) €4.843-451) -(4.8+3.457(48+3.4514 at tro, u z 4 in ( en negative sign is for upward direction) 2 A+B 2-4 at t20, e dez 2. (-4.8 73.451) A -(4-8 +3.45 ;) B = 2 44.8 x4 +3.45 i (A-B) 79 3.45 i (A-3) = -17.2 A-B = 5i 2 A -4+5 Azog+2.5i , B=-2-2.52

UH)= 6-4.871 3.45 t -5i) e +(-2-2.5;).-3.45it 2048 E-a u seosk 453) + 2.5 is ei tine aro? ul> 2.487 [ -400513457) – 5 sine 4.50] in. This is the solution. Please check all the calculations once.