function Homework_3_3360_Spr_2021

clear all

options=odeset('events',@StopSim);

M=1000;K=2000;Vo=24;D=10;g=9.81;

b=0.75*4*M*g/Vo

[t,x]=ode45(@eqns,[0 3],[0 Vo],options);

y=x(:,1);yd=x(:,2);ydd=-(b*yd+K*y)/M;

plot(t,y/D,'r',t,yd/Vo,'k--',t,-ydd/g,'r.','linewidth',2)

grid

xlabel('time, s','fontsize',18)

ylabel('normalized variables','fontsize',18)

legend('normalized displacement, y/D','normalized velocity, y_d/V_o',...

'normalize deceleration, y_d_d/g','location','best')

function dx=eqns(t,x)

Y=x(1);Yd=x(2);

dx=zeros(2,1);

dx(1)=Yd;

dx(2)=-(b*Yd+K*Y)/M;

end

function [Val,Ister,Dir]=StopSim(t,x)

Ister(1)=1;Val(1)=D-x(1);Dir(1)=-1;

Ister(2)=1;Val(2)=x(2);Dir(1)=-1;

end

end

(2) (25%) Execute the MATLAB code provided for this assignment. What are the parameter values used in the code? M= 1000 K = 2000 V. = 24 D= 10 b= 1.2262e+03 For these parameter values, does the design meet the performance specifications? The design did meet the performance specifications Explain why or why not by showing and referring to the plot. Use the 'data cursor'. (3) (50%) By trial-and-error, find the smallest value of b that can be used and still meet the design specifications for the same values of M, K, V, and D. bmin = Use the data cursor to label the peak value of deceleration. (2) (25%) Execute the MATLAB code provided for this assignment. What are the parameter values used in the code? M= 1000 K = 2000 V. = 24 D= 10 b= 1.2262e+03 For these parameter values, does the design meet the performance specifications? The design did meet the performance specifications Explain why or why not by showing and referring to the plot. Use the 'data cursor'. (3) (50%) By trial-and-error, find the smallest value of b that can be used and still meet the design specifications for the same values of M, K, V, and D. bmin = Use the data cursor to label the peak value of deceleration