Odesolve plot notable differences

odesolve divides the interval by default into 10^3 steps.

If the interval runs from 0 to 6 as in your first example, this means timestep is 0.006

But if you increase the interval by the factor 500 as in your last example (t runs from 0 to 3000), the timestep increases by the same factor and is now 3. Of course this usually yields a very inaccurate result.

Solution could be to increase the default value of 10^3 steps - its the fourth (optional) argument of the odesolve function.

Feel free to increase the value significantly more for more precision at the higher values of t.

I guess you (want to) know that the solution to your ode is:

M(t) = cos (t*√3) + √(4/3) * sin(t*√3).

Success!
Luc

As already masters say, it needs number 10^4.