Question

Exercise: MATLAB / Simulink: Use the MATLAB function "ode45" to solve ordinary differential equation mi+bi+kr 0 for the following cases. (for more information about ode45 https://www.mathworks.com/help/matlab/ref/ode45.html) a) m-1, b-1, k-25 b) m 1, b 10, k- 25 c) m1, b-11, k-25 Keep the simulation time 5 seconds and zero initial velocity and the initial displacement 1 for all cases. Plot displacement of the mass x for all three cases in one figure and compare them: which of them decays fastest? Why is that?
Please do not REPOST the same answer as in all of the other ones because they dont work! I keep getting this error When I try to use it

Answer 1

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Save this function file separately

the above program is the actual program to run.

In the above plot blue line corresponds to part (a), dashed line corresponds to part (b) and the other is part(c). Pasting codes below.

%mx''+bx'+kx=0

%initial conditions x(0)=1, x'(0)=0

initial_x=1;

initial_dxdt=0;

t_span=[0 5];

[t,x]=ode45(@(t,x) odesecondorder(t,x,1,1,25),t_span,[initial_x initial_dxdt]);% m=1,b=1,k=25

plot(t,x(:,1));

xlabel('t');ylabel('x');

hold on;

[t,x]=ode45(@(t,x) odesecondorder(t,x,1,10,25),t_span,[initial_x initial_dxdt]);%m=1,b=10,k=25 plotted as dashed line

plot(t,x(:,1),'--')

[t,x]=ode45(@(t,x) odesecondorder(t,x,1,11,25),t_span,[initial_x initial_dxdt]);%m=1,b=11,k=25 plot color yellow

plot(t,x(:,1));

hold off;

function dxdt=odesecondorder(t,x,m,b,k)

dxdt_1=x(2);

dxdt_2=-(b*x(2)+k*x(1))/m;

dxdt=[dxdt_1;dxdt_2];

end