Question

a)by using newtons 2nd law,derive the equation of motion for the vibration system in matrix form
b)diferrentiate between the 1st,2nd and 3rd vibration modes characteristic of the train system based on the mode shape diagram

A three coaches train system shown in Figure 3(a) can be simplified as a three degree of freedoms semi definite mass-spring system as illustrated in Figure 3(b). The masses of the three coaches are /m = 15000 kg, m-10000 kg and m-15000 kg. The three masses are connected in series by two springs having stiffness constant of kk 10000 N/mm. The friction between the coaches wheels and the rail can be neglected Figure 3(a): Three coaches train ki N2 PRI Figure 3(b): Semi definite mass-spring system

Answer 1

Mt o0oo I Sooo 17 -Isooo C1Sooov.tlooo.)k-....어,灬.) (-on°t too..)-t 7 2 1 2

YLiphenau A1 miel