In the present study, numerical investigation is carried out for flow past a transversely oscillating circular cylinder near a wall. A second-order finite-volume method employing diffuse interface immersed boundary method is used to handle the nonconforming boundaries. The cylinder is allowed to oscillate on a fixed Eulerian mesh in order to handle the moving boundary. Simulations are carried out for a number of forcing frequencies at three different gap distances and two amplitudes of oscillation with Reynolds number fixed at 200. While a pair of vortices is found to be shed near the stationary shedding frequency at larger gap distance, multiple interconnected vortices are observed at larger forcing frequencies. Proximity of the wall promotes greater interaction of the wall layer with the near wake resulting in inhibited irregular shedding. Energy transfer changes its direction when the correlation between the cylinder motion and the lift force is strongest. Positive energy transfer attains a peak at the onset of the synchronization regime accompanied by a weaker correlation. Amplitude of oscillation of the cylinder evidently has systematic effect on the drag coefficient and wake fluctuations, though lift force remains grossly unaltered. Lower amplitude of motion favors induced motion as opposed to larger ones where greater negative energy transfer occurs.