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Four masses are connected with spring mass dampers. x1, x2, x3 and xs are the horizontal displacements
of the masses. Derive the equation of motion of the system help_outlineImage TranscriptioncloseXs Х1 к. X2 Хз WИ МИ м. fs (t) M1 M2 Мз В. ВА B2 fullscreen
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Step 1

For the system to be in equilibrium, the sum of the horizontal forces on each mass is 0.

Step 2

By balancing the horizontal forces of mass Ms we get,

Step 3

Similarly by balancing the horizontal forces of masses M1... help_outlineImage TranscriptioncloseМ,х, +(В, + В.)х, -В. х, — В.Х, + (к, +к)х, - кх, - кх,3D0 M2X2+(BB)X- B,X- BX (K K,)X,-K,X- K2X 0 MXBBX, + K2X-K,X,=0 .(II) (KK2) X2-KX- K2X = 0 ..(Ш) (IV) fullscreen

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