I was able to find the maximum velocity and acceleration for part b. However, ha

Question

 I was able to find the maximum velocity and acceleration for part b. However, having difficulty using the fzero function to solve for part c and d. The question for part c and d is listed below in my code.   clear; clc; % (a) In MATLAB, create a matrix consisting of s vs. t, v vs. t, and a vs. % t for 0<=t<=0.01 second. Use 50 subdivions on the t domain. Take r = 9 % cm, w = 100 revolutions per second, and b = 14 cm. Plot s vs. t, v vs. t, % and a vs. t on three separate graphs. % Revolutions Per Second w=100; % [rev/s] % Piston Rod Length b=0.14; % [m] % Time Step dt=.01/50; % [s] % Crackshaft Radius r=0.09; % [m] for k = 1:51     % Time Vector     t(k)=(k-1)*dt;     arg1=2*pi*w*t(k);     term=b^2-r^2*(sin(arg1))^2;     o2=2*pi*w;     % Displacement     s(k)=r*cos(arg1)+sqrt(term);     % Velocity     v(k)=-o2*r*sin(arg1)-(o2*r^2*sin(arg1)*cos(arg1))/sqrt(term);     % Acceleration     term1=-o2^2*r*cos(arg1);     term2Num=-2*o2^2*r^4*(sin(arg1))^2*(cos(arg1))^2;     term2Den=term^1.5;     term2=term2Num/term2Den;     term3=-o2^2*r^2*(cos(arg1))^2/sqrt(term);     term4=o2^2*r^2*(sin(arg1))^2/sqrt(term);     a(k)=term1+term2+term3+term4;     % Applying all into one matrix     Aug=[t;s;v;a]; end % (b) Using MATLAB's max function and the matrix obtained in part (a), % determine the approximate maximum velocity and maximum acceleration in % one revolution, and print out those values. 

     Vmax=max(v);     Amax=max(a); 

 % (c) Using MATLAB's fzero function, determine the time when the velocity of the piston reaches 1/2 of its maximum velocity. 

 % (d) Using MATLAB's fzero function, determine the time when the acceleration of the piston reaches 1/2 of its maximum acceleration. 

Explanation / Answer

%  X = FZERO(FUN,X0) tries to find a zero of the function FUN near X0,
% if X0 is a scalar. It first finds an interval containing X0 where the
% function values of the interval endpoints differ in sign, then searches
%that interval for a zero. FUN is a function handle. FUN accepts real
% scalar input X and returns a real scalar function value F, evaluated
% at X.

% (c).

region =[0 0.01];

f1= @(t) (-o2*r*sin(2*pi*w*t)-(o2*r^2*sin(2*pi*w*t)*cos(2*pi*w*t))/sqrt(b^2-r^2*(sin(2*pi*w*t))^2)-Vmax /2);

x1= fzero( f 1, region);

% (d).

x1= fzero( f , region);

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