Question

The positice as a fncticn of tine attc)of a sqanel naming on a grass field is givn by 4) Flot the rjectoy (positn) of the sqairel for 8) Plot (a second pio) the length of the position c) Flot (aid plot) be angle ) of the position vector for Osrs 30s Question 5: The cymamic storage modulus G and loss modulus G are measures of a material mechanical response to harmonic loading. For many biological mate- rials these modeli can be described by Fung's model: where o is he frequency of the barmocic loading, and G.., , and t, are materialomstens Plod nd G" vess。(two separate plots on the same page) for G. 5b, c'e aas, ti 0.05s, and t:"500s. Let vary between 0.0001 and 1000 s. Use log scale for the o axis

Answer 1

%4

t=linspace(0,30,1000);
x=-.28*t.^2+6.5*t+61;
y=.18*t.^2-8.5*t+65;
r=sqrt(x.^2+y.^2);
theta=atand(y./x);
figure
plot(x,y,'g')
title('Squirrel''s trajectory')
figure
plot(t,r,'k')
title('Length of position vector')
legend('length of r(t)')
figure
plot(t,theta,'r')
title('angle of position vector')
legend('\theta(t)')

%5

G=5;
c=.05;
t1=.05;
t2=500;
w=linspace(.0001,1000,1000);
Gd=G*(1+(c/2)*log((1+(w*t2).^2)./(1+(w*t1).^2)));
Gdd=c*G*(atan(w*t2)-atan(w*t1));
subplot(2,1,1)
semilogx(w,Gd)
title('G'' versus \omega')
xlabel('\omega')
ylabel('G''')
subplot(2,1,2)
semilogx(w,Gdd)
title('G'''' versus \omega')
xlabel('\omega')
ylabel('G''''')