We have a machine element as a springmassdamper system my b

We have a machine element as a spring-mass-damper system my\" + by\' + ky = 0 y(t) = q e^-0.7t cos w t in w = 4 rad/sec use the graphical method to estimate the time required for the displacement to decrease to 3.5 mm hand in the plot with a sketch showing the root location. Use newton-Raphson function from in numerical methods text if find time hand in calculations for y\'(t) print out results, root, epsilonPa, # of iterations use format long

Solution

x=-5:.05:5;

x=x(:);

t3=.75*ones(length(x),1)+.25*x-2*x.^2+x.^3;

xn=-5;

xo=10; % final error criterion

e=.0001;

% plot the function

f2=figure;

fx=xn^3-2*xn^2+.25*xn+.75;

plot(x,t3, ’--’, xn, fx, ’s’)

set(gca, ’FontSize’,16);

xlabel(’x’, ’Fontsize’,16);

ylabel(’f(x)’, ’Fontsize’,16);

set(gca, ’XTick’, -5:.5:5);

title([’Newton-Raphson Method (from ’, num2str(xn), ’)’], ’Fontsize’,16)

grid on

hold on

% do the iteration until convergence

while abs((xn-xo)/xn) > e

fx=xn^3-2*xn^2+.25*xn+.75;

fpx=3*xn^2-4*xn+.25;

xn=xn-(fx)/(fpx);

plot(xn, fx, ’s’);

pause

end