Abstract

The simple pendulum experiment investigates the relationship between the length of a pendulum and its period of oscillation to verify the theoretical formula shown as figure 1 ​​. As seen here, the results show that the period increases with the square root of the pendulum length in order to confirm the direct relativity predicted by the formula. Additionally, the experimental data allowed for an estimation of the gravitational acceleration (g), which closely aligns with the theoretical value of 9.8 m/s squared. The experiment aims to minimize the error due to the air resistance, angle of displacement, and measurement inaccuracies to ensure reasonable results. This study depicts fundamental principles of motion and aims for understanding oscillatory systems in physics.

Fig. 1

Introduction

Ever watched a clock with a swinging pendulum and thought that there is a formula behind it? Well, it turns out, there is more science behind that swing than you’d expect.When you pull it back and let it go, the pendulum swings back and forth in a predictable rhythm. But here is the twist: the time it takes for one swing( T = period ) isn’t affected by the weight of the object or how far you pull it. It mostly depends on how long the string is and gravity.We’re here to make sense of it. In this experiment, we’ll change the length of the string gradually, measure the time for a few swings, and see if the pendulum follows the rules of physics or if it decides to freestyle.Consequently, let’s set up our swinging string, start the stopwatch, and let gravity do its thing.

Materials

• String (non-stretchable)
• Small metallic mass (object)
• Stopwatch
• Meter scale
• Clamp stand
• Protractor (for angle measurement)

Methods

1. Setup the Pendulum – Attach a metallic object to one end of a string and secure the other end to a fixed support in order to make sure there is no any detachment 

2. Measure Length (L) – Measure the length of the pendulumWe adjusted everything so that the length of the pendulum to be .25 until 1 meter.

3. Initial Displacement – Pull the object to a small angle (from 3 to 5°) and release it gently.

4. Measure Time Period (T) – Use a stopwatch to measure the time taken for 5 complete oscillations.

a.Film the pendulum’s motion using a camera to measure the period.

b. Measure the time taken for 5 complete full swings to minimize uncertainty. 

c. Calculate the average time per full swing by dividing the total time by 5.

d. Repeat the measurement five times for accuracy.

5. Repeat for Different Lengths: Change the length of the string and repeat the experiment.

Results

Fig. 2

Figure 2 shows the results as we gradually increasing the length as well as the angle

1. The angle of release for all trials was from 3 to 5 degrees
2. The measured periods ranged from 1.00 s to 2.84 s.
3. Calculated value of g is constant 9.81 m/s².

Discussion

The accepted value of g near Earth’s surface is approximately 9.8 m/s². The experiment that we did determined values are approximately the same, suggesting that there are no any systematic errors in the setup or external influences because, the stopwatch was accurate, there was no elongation of the string because it was not stretchable which resulted in an accurate result as expected. Also, the use from 3 to 5 degree angle was essential for the experiment to succeed as known as a small angle for precision and accuracy.

Conclusion

To conclude the experiment, there was a notice of direct effect relationship between period and length. As the period increases as the length of the pendulum increases. However, any unexpected result in the expected period could result from experimental factors, such as air resistance, friction, or slightly larger angles exceeding the small-angle approximation. Consequently, length is the most important factor because it is an independent variable after it comes the g = gravitational constant of earth 9.81 m/s^2. At the end, the experiment shows that the pendulum’s period depends on its length and follows the rules of simple motion, with small angles will always give better and accurate results.

Sources

Fig. 1

https://www.quora.com/How-is-the-expression-of-a-time-period-of-a-simple-pendulum-when-it-depends-on-the-mass-length-and-acceleration-due-to-gravity

Fig. 3

https://www.cuemath.com/average-formula

Chemistry Tutor and the Use of math to explain the pendulum formula