Question

ECEN 3723 System Dynamics Fall 2019 Homework Assignment #7 Problem 1: The mechanical system shown below is at rest initially. At 1 = 0, a unit-step displacement input is applied to point A (i.e., y(t) = u(()). Assuming that the system remains linear throughout the response period and is critically damped, determine the response.x(i) as well as the values of x(0+), (0+) and (on).

Answer 1

otvAs Given K D 1 slept 777 Por Mechanical syste m md'zlty ) + 6 +Bdilt) +K Z dt Apply ing lap lace translorm -0-25s on both sides yis) MS'xIS) +BSxs) kxes) A+ B+C slep But given yet) utty yis) Step3 Pxom ea Xis (MSt BSt) +19. HB + sMStBStk) 8jA stepy Ghen M Syslem fs citically damped -1) B M K But B 1 M Osts)c

( 3,2 2d) & coitically damped) system slepsRoots -B ase deps 13) 2- &MJ Slep pastfal fraetions M B B B St B M StB steps inverse taplate 1Mutt) UM e B V B V steps: x lo) t2D UM B

step 1o dilt) dt M B Bdf HM B V B te Blamt UMI 2M-BlaMt B M Br te Blamt 2M В dt B ו ת GiELG RUB 9S

RC dxto) +0.e IM ito)= B L stepll: e) ule)-4M BY 2M 2M В o-) -O M BY