Period of Pendulum Lab: Transition from UCM to SHM

[sinthon123]

I am doing a lab report that proves the formula for the period of a pendulum. One part of the assignment requires that I explain how the pendulum goes from UCM (Uniform Circuluar Motion) to SHM (Simple Harmonic Motion). I have described the transition as follows:

"Uniform circular motion requires an object to be moving at a constant speed with a constant radius. The pendulum displays UCM with its constant speed and constant string length. The pendulum is accelerating constantly in UCM because it changes direction. Velocity is changed, and a change in velocity over a period of time creates the acceleration. So therefore, by graphing acceleration on the y-axis and time on the x-axis a characteristic SHM (Simple Harmonic Motion) sinusoidal graph will appear."​

I don't know if I have described the highlighted part correctly... Is it the acceleration that will be graphed or the velocity (since it changes)... The goal here is to show that, using a graph, the characteristic sin graph will be shown. I don't know if graphing my acceleration on the y-axis is going to cause the sin graph to appear. Thank you very much for helping.

 

[$id]

Well for SHM
displacement, velocity and acceleration will vary sinusodically with time. It will not matter which one you plot if all you need is a sinusodial graph. Whether you get a sine or a cosine wave will depend on how you took the data,

 

[wais]

Your explanation of the transition from UCM to SHM is correct. In UCM, the pendulum is constantly accelerating due to the change in direction, which can be seen by graphing acceleration over time. However, in SHM, the acceleration is not constant. Instead, it follows a sinusoidal pattern as the pendulum swings back and forth. This can also be seen on a graph by graphing the displacement or velocity of the pendulum over time. As the pendulum moves from one extreme to the other, the velocity and acceleration change direction, resulting in the characteristic sinusoidal graph. So, both acceleration and velocity can be graphed to show the transition from UCM to SHM, with the sinusoidal graph appearing as the pendulum moves from UCM to SHM. Keep in mind that the exact shape of the graph will depend on the initial conditions of the pendulum (e.g. amplitude, length, etc.) and may not always be a perfect sine curve. Overall, your explanation is clear and accurate. Good luck with your lab report!