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3 consider a piezoelectric sensor shown in the figure below...

Question: 3 consider a piezoelectric sensor shown in the figure below...

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3. Consider a piezoelectric sensor, shown in the figure below (left) along with the equivalent circuit (right). Piezoelectric devices convert electric potential (voltage) into mechanical motion (linear translation) and vice versa. This means that pressing down on the sensor will generate a voltage across the output wires or that applying a voltage to the wires will cause the sensor to move. These sensors are used in many places, such as microphones where they transform mechanical vibrations due to sound waves into electrical signals. in out Co T R (a) The input voltage Vin is directly related to the mechanical force applied to the sensor. Using basio physica equations for the system components, create a set of differential equations that describe the system. Hint: Recal that the voltage drop across a resistor is Ri, across an inductor is Ld, and across a capacitor is C Jidt (you may assume that the capacitors are initially uncharged). (b) Find the Laplace transform of the differential equations from part (a) (c) Using the results of part (b), solve for the output voltage Vout as a function of the input voltage Vin Your final answer should have any other currents or voltages in it, but should depend only on the system parameters (Co, C1, R, L) and the complex variable s. Note: you only need to find the frequency domain solution, you do not have to go back and find the time domain solution

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