Question

(1 point) Consider the initial value problem my" cy' +ky = F(t), y(0) = 0, y'(0) = 0 modeling the motion of a spring-mass-dashpot system initially at rest and subjected to an applied force F(t), where the unit of force is the Newton (N). Assume that m 2 kilograms, 8 kilograms per second, k = 80 Newtons per meter, and the applied force in Newtons is c if 0tT/2, if t > /2 40 F(t)= a. Solve the initial value problem, using that the displacement y(t) and velocity y'(t) remain continuous when the applied force is discontinuous. For 0 t/2, y(t) = help (formulas) For tT/2, y(t) = help (formulas) b. Determine the long-term behavior of the system. Is lim y(t) = 0? If it is, enter zero. If not, enter a function that approximates y(t) for very large positive to0 values of t For very large positive values of t, y(t) help (formulas)

Answer 1

kelo. m 2, C8 mycyky 40, bstEN FIh 2"+ 8y0y L0 Y 4ytoy 4 +oy20 20 y-Syo-0/ Lyes-SIyo) y-yloy0y1s) 2 SS) yis) +404(512 20 .. [ 1 e LO (S+2)%34 S ******* 4Is- 20 2013 October S MTWTFS O 1 2 3 4 5 6 7 8 o 10 11 12 .

26 sy +3 1 Panhiod Frechan parhial trachan t tis 20 stye tL (+473 Yos tS+36 14t-) Los61 t e bt ti - 26 Le 20 40 120 -VLe 2 2. 2lt-N) t +e

foi t tosbt e bt 2 inee tor00 e-t, 21t-h) 70. ....