I How does a harmonic oscillator model have the same frequency

[Fruit Water]

I'm currently studying IR but my mind is having trouble tying everything together.
While I see that vibrational frequency is determined really by just reduced mass, I can see from the equation that vib equation is the same throughout energy levels and so does energy (bc that basically depends on reduced mass and frequency). However, I've seen IR and there's all sorts of crazy spikes and loops and I'm confused on how that ties it together? Like something can have the same frequency but the spikes will be all different? I've tried reading about IR from different sources and something just isn't clicking. I'd seriously appreciate it if someone can clear this up for me!

 

[hilbert2]

You can't model a molecule with many atoms by just using a single harmonic oscillator. For something as simple as carbon dioxide you already have to use a model with coupled oscillators. Another problem is anharmonicity (vibrational energy levels not being equally spaced at high excited states) and rotation-vibrational coupling (higher rotational states having a larger expectation value of internuclear distance because of "centrifugal" effect).