What would the shape of the graph have to be to correctly show the acceleration, of a particle undergoing Simple Harmonic Motion varies with its displacement, from its equilibrium position
The graph of acceleration vs displacement for a particle undergoing Simple Harmonic Motion would be a sine or cosine curve. This is because the acceleration of a particle in SHM is directly proportional to its displacement from the equilibrium position, and is in the opposite direction to the displacement.
As the particle moves away from the equilibrium position, the acceleration increases, reaching a maximum at the maximum displacement from equilibrium. The acceleration then decreases as the particle moves back towards the equilibrium position, reaching zero at the equilibrium position. The acceleration then becomes negative as the particle moves to the other side of the equilibrium position, reaching a minimum at the maximum displacement in the opposite direction.
Overall, the graph of acceleration vs displacement would show a sinusoidal pattern, with the amplitude of the curve representing the maximum acceleration experienced by the particle.