Question

I want matlab code.

585 i1 FIGURE P22.15 22.15 The motion of a damped spring-mass system (Fig. P22.15) is described by the following ordinary differ- ential equation: dx dx in dt2 dt where x displacement from equilibrium position (m), t time (s), m 20-kg mass, and c the damping coefficient (N s/m). The damping coefficient c takes on three values of 5 (underdamped), 40 (critically damped), and 200 (over- damped). The spring constant k-20 N/m. The initial ve- locity is zero, and the initial displacement r- 1 m. Solve this equation using a numerical method over the time period 0

Answer 1

Matlab code for solving ode clear all close all tAnswering question %Initial conditions for ode x0 10]; SAll parameter values k-20, m-20;c-[5 40 200 ] ; for i-1:3 eminimum and maximum time span tspan [0 15 %Solution of ODEs using ode45 matïab function sol-ode45 ( (t,u) odefcn (t,u,m,c(i),k), tspan, x0); Equally splitting time t1-linspace(tspan (1),tspan (end),1001); is the corresponding value for x(1) and X(2) xx 1 = deval ( sol, t1 ) ; legendinfofi) sprintf( C Sd.n', c(i); %plotting x1(t) vs t figure(1) hold on plot (t1, xx1(1,:), 'Linewidth',2) title( Plot for x (t) vs.t' xlabel('time') ylabel(x(t) box on %plotting x2(t) t vs figure (2) hold on plot (t1,xx1(2,, 'Linewidth',2) title( 'Plot for dx (t)/dt vs. t' xlabel(time) ylabel('dx (t)/dt box orn end figure(1) legend legendinfo) Eigure(2) legend (legendinfo) %Function for evaluating the ODE function dudt-odefen (t,x,m,c,k) eq 1 x(2); eq2 (-с/m) *x ( 2 )-( k/m ) *x( 1 ) ; %Evaluate the ODE for our present problem end

Plot for x(t) vs. t -c:40. C-200 0.8 0.6 0.4 0.2 -0.2 -0.4 -0.6 15 -0.8 0 10 time Plot for dx(t)/dt vs. t 0.6 -C15. C-40. C-200 04 0.2 0.4 0.6 0.8 15 10 time

%%Matlab code for solving ode
clear all
close all
%Answering question
%Initial conditions for ode
x0=[1;0];
%All parameter values
k=20;m=20;c=[5 40 200];
for i=1:3
        %minimum and maximum time span
        tspan=[0 15];
        %Solution of ODEs using ode45 matlab function
        sol= ode45(@(t,u) odefcn(t,u,m,c(i),k), tspan, x0);
        %Equally splitting time
        t1 = linspace(tspan(1),tspan(end),1001);
        %x is the corresponding value for x(1) and x(2)
        xx1 = deval(sol,t1);
      
        legendinfo{i}=sprintf('C=%d.\n',c(i));
        %plotting x1(t) vs t
        figure(1)
        hold on
        plot(t1,xx1(1,:),'Linewidth',2)
        title('Plot for x(t) vs. t')
        xlabel('time')
        ylabel('x(t)')
        box on
      
        %plotting x2(t) vs t
        figure(2)
        hold on
        plot(t1,xx1(2,:),'Linewidth',2)
        title('Plot for dx(t)/dt vs. t')
        xlabel('time')
        ylabel('dx(t)/dt')
        box on
end  
figure(1)
legend(legendinfo)
figure(2)
legend(legendinfo)
%-----------------------------------------------------------------%
%Function for evaluating the ODE
function dudt = odefcn(t,x,m,c,k)

    eq1 = x(2);
    eq2 = (-c/m)*x(2)-(k/m)*x(1);
    %Evaluate the ODE for our present problem
    dudt = [eq1;eq2];
end
%-----------------------------------------------------------------%