The complete set of significant normal modes of a single-walled carbon nanotube has been extracted using singular value decomposition analysis of this molecular dynamics data. The first part of this study focuses on an isolated single-walled carbon nanotube performed with NVE Molecular Dynamic simulations. Singular value decomposition analysis is then done on this data. Normal modes are excited with an initial radial stretching given to all the atomic coordinates. For the case with 5% initial radial stretching given to the carbon nanotube, the two strongest modes involve radial breathing motion combined with a very slow rotational motion of individual rings of the nanotube. There is good agreement between the calculated frequency of radial breathing modes and published experimental measurements, as also the inverse scaling of this frequency with tube diameter. The coupling between these two motions weakens for a smaller initial perturbation. The next eight most significant modes are divided into two classes. The first class is characterized by mz = 0, i.e., axial uniformity and produces azimuthal variation in the radial positions of atoms, with a finite azimuthal mode number. The second class of modes has mθ = 0, with mz = 1 and 2, are with radial uniformity and leads to shifts in the X- and Y-centroid locations of different rings. Mode frequency and the associated spatial distortion are thus obtained for all the above-mentioned modes. Under NPT conditions, similar to laboratory conditions, i.e., at a constant temperature and pressure, mode frequencies change only slightly, but the hierarchy of modes is slightly different. External excitation produced at one of the normal mode frequencies, corresponding to centroid motion with (mθ = 0, mz = 1), shows a significant and steady increase in the amplitude of centroid displacement. Excitation at the second harmonic frequency leads to an initial increase in displacement amplitude, but eventual saturation. These conclusions are important for the application of carbon nanotubes in nanodevices, e.g., as nanomotors.