To identify the Fourier series amplitude spectrum that corresponds to the waveform in the second plot, we can follow these steps:

1. Analyze the Waveform Plot (Second Image):

   • The waveform shows a periodic pattern with visible oscillations.
   • To determine the dominant frequency, count the number of large oscillations within the 100 samples shown on the x-axis.

2. Counting Oscillations:

   • The waveform appears to have around 4 major cycles over the 100 samples. This suggests a low-frequency component that would correspond to a frequency of approximately $\frac{4}{100} = 0.04$ cycles per sample.

3. Matching with the Amplitude Spectra:

   • Each of the amplitude spectra in the first image displays a distinct peak at a specific index, which corresponds to a specific frequency component.
   • The spectra with peaks at lower values of $k$ represent lower frequencies.

4. Interpretation:

   • Since we observe 4 major oscillations, the corresponding frequency component should be relatively low, suggesting a peak at a lower index in the amplitude spectrum.
   • Spectrum B and Spectrum D have peaks near $k = 4$, which matches the frequency we deduced from the waveform.

5. Conclusion:

   • The amplitude spectrum that best represents the waveform is likely Amplitude Spectrum B or D, as they have a dominant low-frequency component at approximately $k = 4$, aligning with the observed oscillations in the waveform.

Would you like further details or clarification on any of these steps?

Here are five questions related to Fourier analysis and this context:

1. How does the frequency of oscillations in a waveform relate to the peaks in its Fourier amplitude spectrum?
2. What does a peak at a certain index in the amplitude spectrum signify in terms of the waveform’s frequency content?
3. Can multiple peaks in the amplitude spectrum indicate multiple frequencies present in the waveform?
4. How does the Fourier transform handle non-periodic or complex waveforms?
5. Why might one choose to represent a waveform in terms of its frequency components?

Tip: Counting oscillations can be a quick way to estimate the dominant frequency of a periodic waveform before performing a Fourier analysis.