Brain Magnetic Resonance Imaging (MRI) is invaluable for non-invasively capturing detailed anatomical and functional information. However, motion artifacts, particularly during brain imaging, can compromise the precision of scans. This study explores motion correction techniques, focusing on the widely-used PROPELLER method and its application to Golden-angle Cartesian Randomized Time-resolved (GOCART) acquisition. While PROPELLER effectively corrects in-plane translation and rotation, its use with cartesian data demands increased sampling. GOCART, a high-speed cartesian sampling scheme, has shown promise in Dynamic Contrast-Enhanced (DCE) MRI, yet its specific artifacts in brain imaging remain underexplored. Our simulation framework assesses PROPELLER correction for translational motion in GOCART-sampled data, examining two motion directions, varied frequencies, and different temporal resolutions. Serving as a vital pre-clinical testing tool, this platform contributes to the optimization of motion correction algorithms, addressing challenges and refining imaging protocols for enhanced diagnostic reliability in advanced brain MRI.