Question

6. Use the method of Laplace transforms to solve the problem. A mass of 1 slug, when attached to a spring, stretches it 2 feet and then comes to rest in the equilibrium position. Starting at 1 = 0, an external force equal to f(t) = 8 sin 41 applied to the system. Find the equation of motion if the surrounding medium offers a damping force that is numerically equal to 8 times the instantaneous velocity.

Answer 1

-MONIKA Dare Pepe No paitianf spag at x) bethe L 21at 6 dompny era 8 times 8 Sinyt 1 o)0, wing taplue T furm Trns tut +16 X(9) S2Xes)-sx o)-20) 8 84) 91tS +8s +16)X3) = 32 S2416 32 + 1 -S S+4)2 tteyt Cos4t 4- Ava

Ho to spit Paahial 3 2 32 CS+D (S+16) (s416)es (h+S CS+412 +(cs+ 02 S4) B C1 ALsu)Cs 3a - 32= AlStys2+16st64) t Blsh) +Csto)lsgsts) 32- A+C) +StuA+Bt8c+DOA +S Ca8+ +64A tt6B +ibD A+cao 64A t16 BE32 4A+B-2 4AtB+800 2 80 ty12 S416