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“Biomechanics of the Human Body” (1) The mechanical behavior of three different tissue types is modeled by a Maxwell body. The tissues undergo sinusoidal deformation with strain profile given as: e = ejwt The mechanical properties of the tissues are as follows: Tissue 1: h = 0.005 Pa•s, E = 1 kPa Tissue 2: h = 0.050 Pa•s, E = 1 kPa Tissue 3: h = 0.500 Pa•s, E = 1 kPa (a) On the same plot, show the magnitude of the complex modulus as a function of frequency (w) from zero up to 107 radians/s. Please use a logarithmic axis for w when presenting your plot. Be sure to briefly describe the frequencydependent behavior of the magnitude (15 points for plot, 8 points for discussion). (b) On the same plot, show the phase of the complex modulus (in radians) as a function of frequency (w) from zero up to 107 radians/s. Please use a logarithmic axis for w when presenting your plot. Be sure to briefly describe the frequency-dependent behavior of the phase (15 points for plot, 8 points for discussion). (2) The mechanical behavior of three different tissue types is modeled by a Maxwell body. The tissues undergo sinusoidal deformation with strain profile given as: e (t) = ejwt The mechanical properties of the tissues are as follows: Tissue 1: h = 0.002 Pa•s, E = 0.2 kPa Tissue 2: h = 0.002 Pa•s, E = 0.6 kPa Tissue 3: h = 0.002 Pa•s, E = 1.0 kPa (a) On the same plot, show the magnitude of the complex modulus as a function of frequency (w) from zero up to 107 radians/s. Please use a logarithmic axis for w when presenting your plot. Be sure to briefly describe the frequencydependent behavior of the magnitude (15 points for plot, 8 points for discussion). (b) On the same plot, show the phase of the complex modulus (in radians) as a function of frequency (w) from zero up to 107 radians/s. Please use a logarithmic axis for w when presenting your plot. Be sure to briefly describe the frequency-dependent behavior of the phase (15 points for plot, 8 points for discussion)

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clc;
clear all;
w = 0:10:10^7;
eta = [0.005 0.05 0.5];
E = 1000;
for i = 1:length(eta)
Complex_Modulus(i,:) = (1i*w*eta(i))./(1+(1i*w*eta(i))/E);
end
figure;
semilogx(w,abs(Complex_Modulus(1,:)),'--k','Linewidth',2);hold on;
semilogx(w,abs(Complex_Modulus(2,:)),'--r','Linewidth',2);
semilogx(w,abs(Complex_Modulus(3,:)),'--b','Linewidth',2);hold off;
xlabel('\omega(rad/sec)');ylabel('Pa');
title('Magnitude of Complex Modulus vs Frequency at different \eta' );
legend('\eta = 0.005 Pa.s','\eta = 0.05 Pa.s','\eta = 0.5 Pa.s');

figure;
semilogx(w,angle(Complex_Modulus(1,:)),'--k','Linewidth',2);hold on;
semilogx(w,angle(Complex_Modulus(2,:)),'--r','Linewidth',2);
semilogx(w,angle(Complex_Modulus(3,:)),'--b','Linewidth',2);hold off;
xlabel('\omega(rad/sec)');ylabel('radians');
title('Phase of Complex Modulus vs Frequency at different \eta');
legend('\eta = 0.005 Pa.s','\eta = 0.05 Pa.s','\eta = 0.5 Pa.s');

eta = 0.002;
E = [200 600 1000];
for i = 1:length...

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