(Solved): 3. Fill in LAB05ex2.m to reproduce Fig. 2 and then answer the following questions. (a) For what min ...

3. Fill in LAB05ex2.m to reproduce Fig. 2 and then answer the following questions. (a) For what minimal time t1 will the mass-spring system satisfy |y(t)| < 0.06 for all t > t1? You can answer the question either by magnifying the MATLAB figure using the magnify button , or use the following MATLAB commands (explain): for i =1: length ( y ) M ( i )= max ( abs ( y ( i : end ))); end i = find (M <0.06); i = i (1) disp ([ '| y | <0.06 for t > t1 with ' num2str ( t (i -1)) ' < t1 < ' num2str ( t ( i ))]) (b) What is the largest (in magnitude) velocity attained by the mass, and when is it attained? Answer by using the magnify button. (c) How does the size of c affect the motion? To support your answer, run the file LAB05ex2.m for c = 20, c = 40, and c = 84. Include the corresponding graphs with a title indicating the value of c used. (d) Determine analytically the smallest (critical) value of c such that no oscillation ap- pears in the solution.