why would the shape of the graph to correctly show the acceleration, of a particle undergoing Simple Harmonic Motion varies with its displacement, from its equilibrium position, be a negative linear regression line
The shape of the graph showing acceleration versus displacement for a particle undergoing Simple Harmonic Motion would typically not be a negative linear regression line.
In Simple Harmonic Motion, the acceleration of the particle is directly proportional to its displacement from the equilibrium position and acts in the opposite direction. This results in a sinusoidal relationship between acceleration and displacement. As the particle moves away from the equilibrium position, the acceleration increases in magnitude but changes direction, leading to oscillations that repeat over time.
Therefore, the graph of acceleration versus displacement for Simple Harmonic Motion would typically show a sinusoidal curve, rather than a negative linear regression line.