Using bisection method to solve vibrations problem

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jeff417 2016-9-17

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/303443-using-bisection-method-to-solve-vibrations-problem

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.