Question

What Affects the Period of a Pendulum ?

Analysis of the data, Part 1 Once you have collected your data, it is time to analyze it! In order to analyze data properly, you must consider uncertainty. This guide will walk you through how to treat uncertainty in your lab. For a more complete guide to uncertainty, see the Error and Uncertainty Guide in Files/Labs Materials.
Presenting the Raw Data GradeScope
Q1.Report all of your raw data in easily readable tables here. Be sure that it is clear what length and amplitude were used for each setup, and how many swings were measured. Be sure to report the actual times measured: do NOT divide a time measured over multiple swings by the number of swings to get the period yet
Estimating Raw Uncertainty Values
You took three types of measurements in this lab: length, amplitude, and time. Using one or more of the methods described in pages 3-4 of the Error and Uncertainty guide, you will estimate uncertainties in each of these measurements. For all questions below, the reasoning is much more important than the final number you choose. GradeScope
Q2.Estimate the absolute uncertainty in your length measurements. Explain your reasoning. GradeScope
Q3.Estimate the absolute uncertainty in your amplitude (angle) measurements. Explainyour reasoning. GradeScope
Q4.Estimate the absolute uncertainty in your individual time measurements. Explainyour reasoning. Note: your estimate should be for the uncertainty in the times you actually measured, which was likely over multiple swings. Do NOT yet estimate uncertainty in the time for a single swing.
Averaging over Multiple Measurements Many of you took multiple measurements with each setup (which was a good idea)! If you did this, you’ll need to do this step. If you took only one measurement per setup, you may skip this section. First, use your spreadsheet to average the measurements for each setup. Do NOT yet divide by the number of swings to get the period.

Answer 1

The period of a pendulum is affected by its string length and the acceleration due to gravity, and is largely independent of the pendulum bob's mass and swing amplitude.

Step-by-step explanation:

The period of a pendulum primarily depends on two factors: the length of the string and the acceleration due to gravity (g). When you double the length of a pendulum, the period increases, specifically, it becomes the square root of two times longer, because the period is proportional to the square root of the length. If the length is decreased by 5%, the period will decrease but not by a strict factor of 5% because the relationship is not directly proportional. Furthermore, the mass of the pendulum bob and the amplitude (or maximum displacement) of the swing have virtually no effect on the period, especially if the amplitude is less than about 15 degrees. This characteristic allows pendulum clocks to remain accurate and finely adjusted, even when the amplitude changes slightly over time.

In a hypothetical scenario where a pendulum is transported from Earth to the Moon, the period would change due to the difference in acceleration due to gravity. On the Moon, gravity is weaker, approximately 1.63 m/s² compared to Earth's 9.81 m/s². Consequently, the period would increase, and the ratio of the new period to the old period can be calculated using the square root of the inverse ratio of the two accelerations.