plotting – how to define an example of ODE that represents an undamped forced oscillator whose time evolution is described by beats


Not really a mathematica problem but here is something to get you going in the Wolfram Language.

eqn = x''(t) + (2 π 100)^2 x(t) == f(t);
ic = {x'(0) == 0, x(0) == 0};
f(t_) := Sin(110 2 π t);
sol = NDSolve(Join({eqn}, ic), {x}, {t, 0, 0.2});
Plot(Evaluate(x(t) /. First(sol)), {t, 0, 0.2})

Plot from oscillator

Here I have made an oscillator with a natural frequency of 100 Hz and then applied a force with a frequency of 110 Hz.

The equation you are after is called eqn. The initial conditions are ic and the force has been defined as f(t).

You should be able to copy and paste that into Mathematica and get the plot I have shown.

Good luck