A set of pure sinusoidal pitch and plunge oscillations for a symmetric airfoil is studied in this paper. A gridless Lagrangian vorticity particle-based solver is used to simulate the unsteady flowfield. Various kinematics chosen here are inspired by the experimental and computational studies presented in earlier works. The Lagrangian tool is used to accurately reproduce the flowfield obtained by earlier experimental results. It follows the experimental trend better compared with some of the grid-based solvers' results from earlier studies. The strength of this tool is its grid-free nature, as the resolution of the grid is a crucial parameter in resolving the unsteady flowfield accurately. This study also investigates the effects of the starting condition in dictating the wake deflection mode at short and long terms and confirms the findings of the earlier works. The effect of mean angle of attack on the wake deflection is also highlighted. One of the main questions considered here is whether there exists a kinematic equivalence between sinusoidal pitch and plunge. Effective angle of attack, quasi-steady criterion, and Theodorsen's criterion of unsteady aerodynamics have been considered here for kinematic equivalence with plunge. The latter two give a reasonably good match both in terms of flowfield and load as was also reported in the literature. This behavior is seen in two different plunge stroke amplitude cases studied here. The success of the quasi-steady and Theodorsen's approach indicates the general wake behavior being an inviscid phenomenon, at least for the chosen range of parameters. Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.