Figure P4.56a shows a Houdaille damper, which is a device
Chapter , Problem 4.56(choose chapter or problem)
Figure P4.56a shows a Houdaille damper, which is a device attached to an engine crankshaft to reduce vibrations. The damper has an inertia \(I_{d}\) that is free to rotate within an enclosure filled with viscous fluid. The inertia \(I_{p}\) is the inertia of the fan-belt pulley. Modeling the crankshaft as a torsional spring \(k_{T}\), the damper system can be modeled as shown in part (b) of the figure. Derive the equation of motion with the angular displacements \(\theta_{p}\) and \(\theta_{d}\) as the outputs and the crankshaft angular displacement \(\phi\) as the input.
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