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  3. problem 4 a hydraulic damper or dashpot device is shown...

Question: problem 4 a hydraulic damper or dashpot device is shown...

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Problem 4. A hydraulic damper or dashpot device is shown in Fig.4. The cylinder is rigidly fixed and the rod and piston have mass m. The displacement of the piston x is measured from the center location of the cylinder, and Vo is the cylinder volume when x--0 (e.g., VI V.-Vo if x0). Several orifices allow hydraulic fluid to flow between chambers 1 and 2 and their total area is Ao. Friction between the piston and cylinder is assumed to be linear and is modeled by viscous friction coefficient b. Derive the complete mathematical model of the damper device for two cases (a) The fluid is assumed to be incompressible, and therefore flow rate in/out of a chamber is always equal to the time-rate of volume or A[Hint: the pressure differential between chambers is a function of velocity i (b) The fluid is assumed to be compressible, and therefore we cannot assume that Q = A i always holds. The pressure time-rate equation must be included in the model Both models must accommodate positive and negative velocity Area, AArea, A Rigid connection Applied force, F P. V Rod +Piston Chamber 1 mass, m Chamber 2 Orifices total area-A Fig.4. Hydraulic damper system Viscous friction, b
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