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Unformatted text preview: Ae/APh 104a Homework Problem Set #3 ISSUED: Tuesday, October 19, 2010 DUE: Tuesday, October 26, 2010 (in class) 1/3 The device shown below is a proposed design for a pressure transducer in which the gage pressure P is indicated by the displacement y . (a) Derive the differential equation relating y and P . (b) If the input P is sinusoidal with frequency , find the steady-state am- plitude ratio and the phase angle of y relative to P . (c) How do the amplitude ratio and phase angle behave in the limits and ? 1 2/3 Lumped element modeling of a microfabricated microphone. Rather than analyze the full, nonlinear system, we will consider a simplified system consisting of the diaphragm alone. A thin, wall-flush diaphragm of area A with an equal static pressure applied to both sides, is used to measure pressure fluctuations. A dynamic pressure load is applied to one side of the diaphragm, which will deflect with velocity v under the applied force, f . You will use a lumped parameter approach (ignoring spatial variations) to analyze the mechanical and acoustic impedances of a microphone-type pressure sensor and their effect on measurement sensitivity...
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