Force and Energy
If we ignore damping effects, we can conclude that there are only three forces acting upon the glider vibrating on the horizontal spring - the force of gravity (down), the support force from the track (up) and the spring force (left or right). The two vertical forces will never do any work upon the glider since they act perpendicular to the direction of its motion; thus, they do not do work upon the glider. Only the spring force can do work upon the glider. But since the spring force is a conservative force, it only serves to change the potential energy into kinetic energy (and vice versa) without changing the total amount of mechanical energy. So if we ignore damping effects, we can conclude that the total mechanical energy (TME) is conserved.
Gravitational Potential Energy
The gravitational potential energy (PEgrav) is the energy stored in an object due to the vertical height of the mass within Earth's gravitational field. Changes in height will cause a change in gravitational potential energy. Since the air track glider is not changing its height, its gravitational potential energy will not change. Any change in potential energy will be due to changes in elastic potential energy (next section).
Elastic Potential Energy
The elastic potential energy (PEspring) is the energy stored in the mass-spring system due to the amount the spring is stretched or compressed relative to its relaxed state. For a horizontal spring, the relaxed state is also known as the equilibrium position. When the mass is at this position, there is no elastic potential energy. As the mass moves further away from this position, the spring stretches or compresses more and the elastic potential energy increases. The amount of elastic potential energy is proportional to the square of the stretch distance. The relaxed state is shown in the top snapshot of the three snapshots of the spring. The further that the mass moves from this position, the more elastic potential energy that will be stored in the system.
Kinetic Energy
The kinetic energy depends upon the speed of the object. As the speed of an object increases, its kinetic energy will increase. The equilibrium position of the mass on the horizontal spring is shown in the top snapshot (marked "Equil."). As the mass moves away from this position, the spring is displaced (stretched or compressed). When located to the right of equilibrium, the spring is displaced to the right and the spring force acts leftward (in the opposite direction of the displacement) on the glider. When located to the left of equilibrium, the spring is displaced to the left and the spring force acts rightward (in the opposite direction of the displacement) on the glider.
So as a glider moves away from its equilibrium position towards one of its two extreme positions (far left or far right), the spring force acts in the opposite direction of its motion and slows it down. And as a glider moves from one of its two extreme positions (far left or far right) towards the equilibrium position, the spring force act in the same direction as its motion and speeds it up. So one can conclude that the speed is greatest at the equilibrium position and lowest (in fact, zero) at its two extreme positions.
Your Best Approach
From the information presented above, make an effort to rule out options. For instance, do any of the three options represent increases or decreases in the total energy? If so, they can be ruled out. Make an effort to determine which location has the greatest KE - A or B - and rule out any option that incorrectly displays this. Do the same reasoning for elastic potential energy. When you are done, there should be only reasonable option left; tap it and collect your Dataway!