I'm currently trying to make an educational aid that would graph the position of an object as derived from a second order differential equation. What I would like is for the graph to change as I change the various constants of the equation.
What I currently have looks like this:
a = Manipulate[
DSolve[{m*x''[t] + b*x'[t] + k*x[t] == 0, x[0] == 5, x'[0] == 0},
x[t], t], {b, 1, 20, .1}, {m, 1, 20, .1}, {k, 1, 20, .1}]
f[t_] = x[t] /. a[[1]];
Dynamic[Plot[f[t], {t, 0, 20}]]
The manipulate works fine, it provides sliders and will output a correctly solved x(t) for the differential for whatever constants I change the sliders to. However, the plot doesn't update as the sliders update. Any advice on how to get the plot to correctly update would be greatly appreciated