Answer
The relation between E and U at turning point will be equal ( E=U) .
Work Step by Step
To find :
We have to find the relation between E and U at the turning point.
So now its calculation parts :
As we all know that the maximum displacement is x=A or x=-A in the opposite direction.
Also, we know that maximum displacement there is no kinetic energy.
Then the total energy will be
$E= K.E + P.E$
$=0 + P.E$
$=P.E$
$=U$
At the displacement x=A.
The slope of $U_{x} is positive $
Then the force $F_{x} < 0$
That force vector F.is in the opposite direction of the displacement.
So the particles is traveling in a +X direction and start to travel in the -X-direction.
At the displacement x=-A.
The slope of $U_{x} is negative $
Then the force $F_{x} > 0$
That force vector F. is in the opposite direction of the displacement.
So the particles is traveling in a -X direction and start to travel in the +X-direction.
