As a mass on a horizontal spring vibrates back and forth, there are periodic changes in speed and the amount the spring is stretched or compressed. Since kinetic energy depends upon speed and elastic potential energy depends on the amount the spring is displaced (stretched or compressed) from its relaxed state, there are naturally changes in these forms of energy. Energy bar charts are a tool for representing these changes in energy forms.

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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 (PE_grav) 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. 


Elastic Potential Energy
The elastic potential energy (PE_spring) 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.  



Advice About Bar Charts
The bar charts in this question represent the amount of kinetic energy and potential energy possessed by the air track glider. The height of each bar is representative of the amount of that type of energy. A location where the glider possesses a lot of kinetic energy will be described by a taller KE bar. A location where the glider possesses no kinetic energy will be described by a smaller (zero) KE bar. The same can be said for potential energy. 
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Our first piece of advice about bar charts is make sure you understand the content in the previous four sections on this page. There is no short cut to understanding a bar chart that avoids these four sections.

Our next advice is to take your time and analyze the movement from location A to location B. Ask:

• In which location - A or B - is the spring stretched or compressed the most? Compare the distance the glider is from Equil.
• Does the PE (elastic) increase or decrease in going from location A to location B?
• In which location - A or B - is the glider moving the fastest?
• Does the KE increase or decrease in going from location A to location B?

You will use information from the Potential Energy and the Kinetic Energy sections above to answer these questions. Once you've answered these questions, you can rule out a number of incorrect options and narrow the potential answers down to one or two options. Then when you consider the conservation of total energy, you will be able to isolate the correct answer from the remaining options.