Characterizing the conformational properties and dynamics of biopolymers and their relation to biological activity and function is an ongoing challenge. Single molecule techniques have provided a rich experimental window on these properties, yet they have often relied on simple one-dimensional projections of a multidimensional free energy landscape for a practical interpretation of the results. Here, we study three short peptides with different structural propensity (alpha helical, beta hairpin, and random coil) in the presence (or absence) of a force applied to their ends using Langevin dynamics simulation and an all-atom model with implicit solvation. Each peptide produces fluctuation power spectra with a characteristic dynamic fingerprint consistent with persistent structural motifs of helices, hairpins, and random coils. The spectra for helix formation shows two well-defined relaxation modes, corresponding to local relaxation and cooperative coil to uncoil interconversion. In contrast, both the hairpin and random coil are polymerlike, showing a broad and continuous range of relaxation modes giving characteristic power laws of omega(-5/4) and omega(-3/2), respectively; the -5/4 power law for hairpins is robust and has not been previously observed. Langevin dynamics simulations of diffusers on a potential of mean force derived from the atomistic simulations fail to reproduce the fingerprints of each peptide motif in the power spectral density, demonstrating explicitly that such information is lacking in such one-dimensional projections. Our results demonstrate the yet unexploited potential of single molecule fluctuation spectroscopy to probe more fine scaled properties of proteins and biological macromolecules and how low dimensional projections may cause the loss of relevant information.