Two identical gliders on an air track are connected by an ideal spring. Could such a system undergo SHM? Explain. How would the period compare with that of a single glider attached to a spring whose other end is rigidly attached to a stationary object? Explain

A simple harmonic motion is characterized by a trajectory that can be described by the trigonometric functions, sine, and cosine. There are a lot of motions that can be described by simple harmonic motion, such as the motion of a swinging simple pendulum.

Since the two gliders are connected to the same spring, and since we assume that the air track is frictionless, so the system could undergo a simple harmonic motion. at the same time.

Noting that during this simple harmonic motion of the two gliders, the whole system might have a linear motion on the air track unless you nailed the spring from the middle to the track.Noting that the forces exerted on each glider by the spring is the same.

In the second case, when you attach one glider to the spring and the other end of the spring is hooked to the wall:

If you compressed the spring the same distance you compressed it in the first case above, so the force exerted on the glider will be as same as the force exerted on the two gliders of the first case.

Hence, the glider will have the same SHM and the same periodic time.

To make sure, remember Newton's third law. When you push the two gliders by some force F, as mentioned above,as mentioned above, then the spring respond by the same amount of force in the opposite direction.This means that the two cases are similar since the spring will exert a force F on the right and left gliders in the first case, and exerts the same force on F the glider and thewall in the second case.

The only different thing, in the second case, is that the wall will not move.