Figure P2.18 shows a simple model of a mass, two springs, and a damper. Derive t

Question

Figure P2.18 shows a simple model of a mass, two springs, and a damper. Derive the

differential equation that relates the input force F to the motion of the mass x. The final

differential equation should have only x and F as variables; there should be no extraneous

coordinates in the final equation.

Please provide clear steps. Thanks!

Spring-mass-damper system with two springs. shows a simple model of a mass, two springs, and a damper. Derive the differential equation that relates the input force F to the motion of the mass x. The final differential equation should have only x and F as variables; there should be no extraneous coordinates in the final equation.

Explanation / Answer

as

Mass x acceleration = external force - counteracting damper force
Spring force = damper force (= reaction force on the fixed 'wall')
K1x1=bx1'.

final equation become like this

Mx''+(k1+k2)x=F.

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