Simple simple harmonics question

[northern expo]

"simple" simple harmonics question

in a recent lab experience of simple harmonics, pendulum motion, we find that as the length of the pendulum is deceased the period changes but the real question is about the velocity of the pendulum as the length is decreased. when graphing the length over the period you find that the velocity appears non linear as the length changes linearly. when graphing the length over the period^2 we find the data results are very linear which is expected. i need some concrete evidence to what is happening to the velocity as the length changes linearly. is the velocity changing linearly or is this a quadratic function between the length and period (T)??

 

[LightHero]

The velocity of the pendulum is not changing linearly as the length is decreased, but rather it is following a quadratic function between the length and period (T). This can be seen by graphing the length vs the period squared, which will produce a linear graph. The general equation for this relationship is T^2 = 4*pi^2*L/g, where L is the length of the pendulum and g is the acceleration due to gravity.

 

[astrokreng]

Based on the information provided, it appears that the velocity of the pendulum is changing non-linearly as the length is decreased. This can be seen in the graph of length over period, where the data points do not fall on a straight line. However, when the period is squared, the resulting graph shows a linear relationship, which is expected for simple harmonic motion.

This suggests that the velocity of the pendulum is not changing linearly, but rather follows a quadratic function. This is likely due to the fact that the pendulum's velocity is affected by both the length and the period, which are both changing as the length is decreased. As a result, the relationship between the two variables is not linear.

To further investigate this, you could conduct additional experiments with varying lengths and measure the velocity at each length. This would provide more concrete evidence for the relationship between velocity, length, and period in simple harmonic motion. Additionally, mathematical calculations and equations can also be used to determine the exact relationship between these variables. Overall, this is a fascinating topic in the study of simple harmonic motion and further research and experimentation can help to better understand the behavior of the pendulum.