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and velocity the rate change displacement with tim

And velocity the rate change displacement with time

798

F

y

Mass

F

where c is a constant.

3. Mass

F
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Control and Instrumentation Systems

Displacement y

(a) Applied Mass Force Mass

Dashpot

(b)

Spring

mass becoming involved, the
forces and displacement are

force

horizontal. The rollers enable

Solution
To obtain the system model we draw free-body diagrams, these being diagrams of masses showing just the external forces acting on each mass. For the system in Figure 18.84(a) we have just one mass and so just one free-body diagram and that is shown in Figure 18.84(b) . As the free-body diagram indicates, the net force acting on the mass is the applied force minus the forces exerted by the spring and by the dashpot:

net force � F ky

c dy
dt

m d y dt 2� F ky
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