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HW2_Soln - 1 2 BENG 186B HWK#2 Matlab code for...

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3 % BENG 186B HWK #2 % Matlab code for problem #1 (can copy and paste into Matlab workspace or % save it as a .m file and run it % % Questions to be addressed to: [email protected] % Plot of the magnitude of the transfer function as a function of ? = [0 -> % 100] for 5 different R values between R=1-10? clear all ; % clear all variables close all ; % close all opened figures clc % clear screen w = 0:1:100; % w ranges from 0 to 100 with step intervals = 1 a = @(R) ((5 + R) .* R .* w.^2) ./ (4 + (5 + R)^2 .* w.^2); % define a as a function of R b = @(R) (2 * R .* w) ./ (4 + (5 + R)^2 .* w.^2); % define b as a function of R TF = @(R) a(R) + b(R) * i ; % define the transfer function as a function of R magTF = @(R) abs(TF(R)); % magnitude of the transfer function (also a function of R) : abs(a + bi) = sqrt(a^2 + b^2) figure(1); ColorMap = [ 'r' , 'g' , 'b' , 'k' , 'c' ]; % define a colormap to be able to differentiate plots for different values of R i = 1; % counter that will be used as an idex for the colormap for Romega = 1:2:10 % Romega varies between 1 and 10 with step intervals = 2 => 5 values in total plot(w, magTF(Romega), ColorMap(i)); % plot of magTF as a fcn of w (notice that magTF(Romega) is equivalent to magTF(1), magTF(3) .... i = i + 1; % increment counter hold on ; % keeps same plot for the other values of R instead of creating a new plot for each (effect can be tested by omitting this line) end ; legend( 'R = 1' , 'R = 3' , 'R = 5' , 'R = 7' , 'R = 9' ); hold off ; xlabel( 'w(rd/s)' ); % display labels and title ylabel( '|V_{out}/V_{in}|' ); title( 'Magnitude of the Transfer Fcn V_{out}/V_{in} as a function of the angular frequency w' );
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4) (14 points) A piezoelectric sensor is made of quartz and is rectangular in shape with a thickness of 2mm and sensor area of 5cm 2 . It is used to measure applied force (in grams) in terms of output voltage (in mV). What is the static sensitivity of the sensor? Equation: v = kf = kfx +5 points Remember that f = ma (or mg in this case) C ε 0 ε r A k = 2.3 x 10 -12 C/N ε 0 = 8.8 x 10 -12 F/m ε r = 3.7-4.5 ( -2 pts for using ε r = 1) **Note: Must look up value for ε r . Credit given for correctly back-calculating ε r from example in the book, however this value is much higher than the typical values.
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