Question
Asked Sep 25, 2019
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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

Xs
Х1 к.
X2
Хз
WИ
МИ
м.
fs (t)
M1
M2
Мз
В.
ВА
B2
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Xs Х1 к. X2 Хз WИ МИ м. fs (t) M1 M2 Мз В. ВА B2

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Expert Answer

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,

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MX,B,XX + KX -KX (t) .I)

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Step 3

Similarly by balancing the horizontal forces of masses M1...

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М,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)

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