Understanding the low-frequency normal modes of amino acids, the building blocks of proteins, is crucial to reveal the vibration-function relationship in the macromolecular system. Recent advances in terahertz spectroscopy (THz) and solid-state density functional theory (DFT) have ensured an accurate description of low-frequency modes of amino acids. New knowledge people have learnt so far is that the inter- and intra-molecular vibrations are strongly mixed with each other in the THz region through the vibrational coordinate mixing. Rich information is believed embedded in this phenomenon. We introduce a generalized mode-analysis method that allows for the accurate decomposition of a normal mode of interest into the three intermolecular translations, three principal librations and various intrinsic intramolecular vibrations. This mode-analysis method will be demonstrated in the crystalline C60 systems and then applied to shed light on the nature of low-frequency phonons of glycine, diglycine and triglycine. This method helps reveal new intramolecular vibrational modes on the first hand, and more importantly, illuminate a new phenomenon of the frequency distribution of intramolecular vibrations (FDIV). FDIV describes the possible broad distributions of important intramolecular vibrations in the low-frequency normal modes. The FDIV concept may indicate an additional mechanism for the intramolecular vibrations to become thermally active and participate in various biological functions.