Using bisection method to solve vibrations problem
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For my numerical methods class, we use MATLAB to solve all problems. I already have the bisection method code:
if true
function [x] = bisection(fun,a,b,maxtol,maxitr)
if nargin<5, maxitr=50; end
if nargin<4, maxtol=0.001; end
x = a;
k = 0;
fprintf('\nIter#\ta\t\t\tf(a)\t\t\tf(b)\t\tf(x)\n');
while k < maxitr && (abs(fun(x))) >= maxtol
k = k+1;
x = (a+b)/2;
if(fun(a) * fun(x)) < 0
b = x;
else
a = x;
end
fprintf('\n%i\t\t%f\t%f\t%f\t%f\t%f\t%f\n', k, a, fun(a), fun(b), fun(x))
end
For my problem, I have the solution as:
x(t) = x0*(exp(-ct/2m))*cos(sqrt((k/m) - ((c/2*m)^2)*t))
where t at t=0, x = x0.
I also have:
frequency: w = sqrt(k/m - (c/2*m)^2)
period: T = 2*pi / sqrt((k/m)-(c/2*m)^2)
critically damped: k/m - (c/2*m)^2 = 0
overdamped: k/m - (c/2*m)^2 < 0
I've been given values for k, c, and m.
My goal is to use the bisection method to find the time instants when the displacement is 5% of the initial displacement. I need the first three solutions.
I have no idea how to solve this, or even begin.
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