Sorry if this is a stupid question, but I can't seem to understand this. According to the acceleration-displacement graph(Attached IMG), why is the acceleration of a body performing SHM at max amplitude with Max acceleration when speed at that point is zero(Due to no Kinetic energy, and Max potential energy)?
At maximum displacement the particle has stopped moving.
Q: So which way would you like the particle to go?
A: In the negative x-direction back towards the origin.
This means the direction of the acceleration must be in the negative x-direction.
SHM is all to do with motion about a point with a force (acceleration) which is always trying to get the particle back to that point.
The "trouble" is that the particle gets to the point with a finite velocity when the force (acceleration) is zero and overshoots that point.
So the direction of the force (acceleration) reverses in an attempt to get the particle back to the point again leading to failure.
Speed is 0 at the point of maximum dislacement about mean position, but acceleration is the rate of change of velocity. The velocity reverses the direction at that point so its rate of change is maximum. This is the reason for maximum in the opposite direction of displacement.
Moreover we get it from the equation of SHM that acceleration is directly proportional to negative of displacement about mean position.