A unique atomic structure of carbon nanotube unveils outstanding properties. This makes it potentially highly valued reinforcing material to strengthen composite materials. The methodology is established in this research paper to investigate the static and dynamic characteristics of the nanocomposites. Repol polypropylene H110MA is used as a matrix material along with the different percentages of single-walled carbon nanotubes (SWCNTs). A concept of representative volume element (RVE) is considered to study the various properties of the nanocomposite material. The carbon-carbon bond of nanotube is modeled using Tersoff-Brenner potential and represented by space frame element. The matrix material properties are tested in the laboratory which are further used to model it and represented by three-dimensional continuum elements. The interaction between nanotube and polymer matrix is modeled using "Lennard-Jones 6-12" potential represented by nonlinear spring elements. The effect of reinforcement, chirality, % volume of SWCNT, atomic vacancy defect and Stone-Wales defect on the properties of nanocomposite are investigated. To see the effect of reinforcement, the eigenvalues of the RVE are extracted for different boundary conditions. The viscoplastic behavior of the matrix material is considered and the rate-dependent characteristics of the nanocomposite are studied. The damping property of the nanocomposite material is also investigated based on the phase lag between stress and strain field by applying harmonic strain at different frequencies.