The present study investigates flow characteristics of two-dimensional (2D) vortex-induced vibrations (VIV) of the flow past an elastically mounted circular cylinder using OpenFOAM. A low value of Reynolds number (Re = 150), a zero value of damping coefficient (ξ = 0) with a low value of mass ratio (m* = 2) have been taken to examine the wake characteristics for a fixed range of reduced velocity (Ur), ranging from 3 ≤ Ur ≤ 8. Vorticity contour has been presented to study the vortex shedding pattern behind the cylinder and unsteady wake flow for different values of Ur. Amplitude responses, synchronization regime, and time series of amplitude of transverse oscillation corresponding to lift coefficient (Cl) for different values of Ur have been studied. Hilbert spectral analysis has been used for unsteady periodic oscillations and to find the effect of Ur on wake transition for the signal of transverse velocity in the wake. Marginal and Fourier spectra have been used to analyze the frequency of wake-shedding, and it also helps to analyze the distribution of wake-shedding frequency in energy frequency domain. A comparison of the two spectra illustrates that even the lowest frequency can be extracted by using marginal spectra, which otherwise cannot be captured in Fourier spectra. Changes in the mean drag (Cdmean) and lift coefficients (Clrms) for different values of Ur have also been reported.