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Rotating Drum The figure below shows a uniform cylindrical drum (of radius R) having moment of inertia 1cm about the axis (O) passing along the axial of the drum as shown coming out of the page in the middle of the figure. The fixed axis O is coming out of the page A chain of uniform linear mass density P and total mass m is wrapped one complete turn around the drum. In static equilibrium, the chain ends are at 0 = 0 with one fixed to the drum and the other loose. A small ball of mass M is now attached at rest to the loose end of the chain causing the chain to unwrap away from the drum as the drum rotates clockwise about O. Assuming that the drum rotates freely (no friction) about its axis as the chain unwraps, it can be shown that the angle that the drum rotates satisfies (for 0 < < 2t the ODE 0 = (271++-sin(0))B where 2R A = 2nt + u + mR* 1cm and u = M/m> 0 are unitless quantities. Solve this equation for 0(t) using Matlab assuming the initial conditions 0(0) - 0 and é(0) = 0, and determine (for different values of H > 0) the time (in units of (R/g) when all the chain has unwrapped from the drum. You may assume that the mass of the drum is the same as the mass of the chain and that the drum is hollow so that = mR².

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function time_to_unwrap=P(mu_in)
%function P(mu_in)
%INPUTS:
% mu_in -- an array of values of mu = M/m
%OUTPUS:
% time_to_unwrap -- a sequence of times in units of (R/g)^(1/2)
%       for the chain to unwrap.
% Example P([1:10]) to run in a range of 1 to 10

global g R mu
g=1;%Since we are doing every thing in units of R/g^1/2
R=1;%We can take g=1 and R=1;

%mu=M/m;
for k=1:length(mu_in)
    mu=mu_in(k);
    to_plot=0; %This in case we want to turn on extensive plotting
    time_to_unwrap(k)=find_time_to_unwrap(mu,to_plot);
end
%Print a table of times to unwrap.
fprintf('mu = M/m | Time to unwrap (R/g)^(1/2) \n');
for k=1:length(mu_in)
    fprintf('%g | %g \n', mu_in(k),time_to_unwrap(k));
end...
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