Find the synchronous response to the mass-spring oscillator.

Question

The book says the resonance happens clearly at around $\Omega \approx. 5$, but I'm not quite seeing it just by looking at the graph.

Answer 1

Just plug in your solutions for A and B into the solution form you stated:

$$y(t)=A \cos \Omega t+B\sin \Omega t$$

You can use www.desmos.com. Put a slider on the $\Omega$ value. You'll see the amplitude maximizes around 4.94 a little less than 5.