$(4$ pts$)$ A cart attached to a spring is displaced from equilibrium and then released. There is no friction. A graph of displacement as a function of time for the cart is shown. The arrows and signs above the cart indicate the positive and negative directions for the position of the cart.

For each question below, choose from the labelled points above, or state "none" or "all":

a$.$ At which point$($s$)$ is the spring potential energy at its maximum value?

b$.$ At which point$($s$)$ is the acceleration negative? $$

c$.$ At which point$($s$)$ is the total energy at its maximum value?

d$.$ At which point$($s$)$ is the velocity positive? $$