Question

Figure below shows the time response of the system mechanical figure above to a force in step of 8.5 N.


Following the analysis of the system in the figure above
a) Determine the transfer function X(s)/F(s) of the system and give the standard form of the latter.
b) Based on the response of this system at 8.5 N, determine the ,$\omega _{n}$ and $\zeta$ parameters of the mechanical system.
c) By combining the results found previously, determine the value of the three elements B, m and k of the system.

JВ 1.05 Ns/m x(t) т TITI 0.2 0.18 Time 2.72 sec Displacement : 0.19 m 0.16 0.14 0.12 0.1 Displacement : 0.121 m 0.08 0.06 0.04 0.02 15 25 30 5 10 Time (sec) Displacement (m) 20

Answer 1

bell esptt05 i= fu)-8-ke Ltmit bi+ ke -tlt) kKaptace Trantfero XCS / Fes) msit 6stk Xee) Ta ke whek 2 Gwn Fes k St S4andard Fosm Gnen fit) =2-5 Fes2= 5 ,Take Partinl Faactions 2-5 S Cs+ D A XCS)= Aut 8. 5P A= 8-5P. C+A= 0 C--35P, 0+2914mA= 0 22 D= -2ehx 8-5P X

8.5p 8:5P St Rewn wm Ls42gwns a Inverse Loplace 8.5P St 29On 3-5P StGwn l st2gwastwn St Giun Wn iny n wd cos wst ashere Pa O.121 8.5 - = 70 .26 Nm o 121 Peak time R-72-sec tp tora Second ooler ystem d-72 oveaghoot 019m ss= 121 o.19-a12/ %overghoot X100057.42 57

57-0257=ビ XIOO -G7 Co.570157 >in >G2C0.315s) = 0-3)55 1-15 15 wn 169ndis wn 1-168 k 70.2S T0 25 51-oky 1.1682 Here b Beff Rdo176メ1-169 Bolt 51.5 =81.173 Ceff 6+1-05ニス1173 eERo 123 NS m