SHM or Not??

Animation 1

Animation 2

Animation 3

Animation 4

Animation 5


A ball on an air track is attached to a compressed spring as shown in the animations (position is in meters and time is in seconds). Each of the 5 graphs CORRECTLY shows a different property of the motion of the ball.


Determine whether the green ball undergoes simple harmonic motion and state which graph(s) tell you this.


Instructor Resources

Reference: See Giancoli-PA: 11-1, Giancoli-SE: 14-2.
Answer: Animation 5. Most students will think that this motion is simple harmonic motion when they see the sinusoidal position vs. time graph (students often perceive that a sinusoidal x vs. t graph proves simple harmonic motion instead of a linear restoring force having a sinusoidal x vs. t graph). They are still relatively convinced of simple harmonic motion when they see a v vs. t graph, which still looks sinusoidal. However, the force vs. x graph (here the acceleration vs. position graph) is what tells us whether the force is a linear restoring force and whether we have simple harmonic motion. Here we do not have a linear restoring force with the amplitude of motion shown.
Script Author: Mario Belloni