= Solution
The source text and its figure are inconsistent here. \b[The plotted low-frequency maximum in W is near $0.0055\,\mathrm{day^{-1}}$, rather than the printed $0.055\,\mathrm{day^{-1}}$.] The original PDF shows that this discrepancy is already present in the examination, rather than introduced by transcription.
Machine 2 records only about half a year. Its first nonzero <discrete Fourier transform> bin is therefore at
$$
\Delta f\simeq\frac1{180\text{--}183\,\mathrm{days}}
\simeq0.0055\,\mathrm{day^{-1}}.
$$
The annual component near $1/365\,\mathrm{day^{-1}}$ is below that first bin. The finite <window function> spreads it through <spectral leakage>, with a prominent first-bin contribution. This explains the plotted peak without invoking a new physical period.
A literal peak at $0.055\,\mathrm{day^{-1}}$ would instead have a period of about $18.2$ days. Neither the two stated model frequencies nor the given sampling schedule identifies such a separate component. The interpretation above treats the printed decimal as an apparent typo; it does not silently change the stated number.
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