How to find velocity and position of this ODE

Hello all.

I've been trying to find the velocity and position of an object with an accelration rate of a(x)=-2x+1 m/s^2 with the initial conditions of v(0) = 4 m/s, and x(0) = 5 m, all at a time of 5 seconds.. I did my code on it, and believed to have found position with my current plot, however I can't seem to figure out how to calculate and plot my x versus t graph for velocity. Can someone help me out please?

Code below:

[T,s]=ode45(@eom,linspace(0,5,101),[5,4]);
plot(T,s(:,l),'-k')
xlabel('Time, sec')
ylabel('x,m')

function ds=eom(T,s)
ds(1,1)=s(2)
ds(2,1)=-2*s(1)+1
end

%Above function was for position, which seems to work.

%Below was my attempt at the velocity plot.

function ds=eom(T,s)
ds(1,1)=s(2)
ds(2,1)=-2*s(2)^2+s(1)_
end

Answer 1

[David Goodmanson]

Hi Peter,

since you have defined s(2) = ds(1)/dt, s(2) is the velocity function already. No more work required, exceptto plot it,

[T,s]=ode45(@eom,linspace(0,5,101),[5,4]);
plot(T,s)
xlabel('Time, sec')
legend('x, m','v ,m/s','location','southeast')

function ds=eom(T,s)
ds(1,1)=s(2)
ds(2,1)=-2*s(1)+1
end

Here the plot function plots out the colums of s independently, so you get x and v.

[madhan ravi]

ode45 with no output arguments plots by default thereby avoiding the plot call.