$$x''+9x=\sin(3t),$$
$$x(0)=x'(0)=0.$$
This question was asked on a test. We are allowed to solve differential equations with TI-89.
My steps:
- Solve with TI-89, solution $$x(t) = \frac{1}{18} (\sin(3 t)-3 t \cos(3 t)) .$$
- Plot the solution, and then look at the graph, and decide whether it's a beat or resonance.
Apparently, we are not allowed to solve the equation. How can i decide whether this IVP produce beat or resonance?