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Neural networks exhibit a pronounced spectral bias, preferentially converging to low-frequency components of target functions while struggling with high-frequency details, as governed by the neural tangent kernel and the frequency principle. In the domain of materials science, accurate prediction of atomic forces in periodic crystals is essential because high-frequency force components directly encode short-wavelength phonons that govern thermal transport, lattice thermal conductivity, phonon dispersion relations, and mechanical stability under strain. Periodic crystal graphs, formed by atoms connected through cutoff-based edges under periodic boundary conditions, amplify this spectral bias relative to molecular graphs or Euclidean data: the discrete spectrum of the graph Laplacian introduces pronounced gaps between low- and high-eigenvalue modes, and standard message-passing layers act as repeated low-pass filters that exponentially attenuate high-frequency signals. We develop a theoretical framework that decomposes force fields into graph-Laplacian eigenbasis components, couples the training dynamics to the neural tangent kernel on the crystal graph, and derives bounds on high-frequency force prediction error that grow exponentially with the spectral gap of the crystal graph. This analysis reveals why conventional graph neural networks systematically miss high-frequency forces and provides rigorous mathematical mechanisms—over-smoothing, spectral-gap bottlenecks, pooling-induced filtering, and limited receptive fields—that explain the failure. The resulting bounds and propositions imply concrete architectural modifications, including residual high-frequency pathways and spectral preconditioning, that can mitigate bias while preserving the inductive biases required for periodic materials modeling.