Verification of the Relationship between Time Period (T) and Length (L) of a Pendulum

Objectives: Verification of the Relationship between Time Period (T) and Length (L) of a Pendulum

Simple Pendulum Experiment - Lab Notes

🧪 Simple Pendulum Lab Experiment

Investigating the relationship between Time Period and Length

🎥 Real Lab Demonstration

📘 Theory & Formula

A simple pendulum consists of a mass (bob) suspended from a fixed point by a string of length L. It swings back and forth under the force of gravity. The time it takes for one full oscillation is called the time period T.

The time period is given by the formula:

T = 2π √(L / g)

  • L: Length of the string (in meters)
  • g: Acceleration due to gravity (9.81 m/s²)
  • T: Time period (in seconds)

📊 Observed Results

Measurements of 20 oscillations and time period calculation:

Length (L) m Time for 20 Oscillations (s) Time Period T (s) T² (s²)
0.322.01.101.21
0.528.41.422.02
0.836.01.803.24

📈 T² vs Length Graph

📝 Experimental Notes

  • Keep oscillation angle <15° to apply the simple harmonic motion model.
  • Use stopwatch to time 20 oscillations, then divide to get T.
  • Ensure the bob is small and string is inextensible.

✅ Conclusion

The experiment confirms that the square of the period (T²) is directly proportional to the length (L) of the pendulum. The plotted graph T² vs L is linear. This matches the theoretical prediction from the formula T = 2π √(L / g).

Reference Book: Tanzania Institute of Education. (2009–2013). *Physics Book 1–4*. Dar es Salaam: TIE. Ngoma, D. K. (2012). *Practical Physics for Secondary Schools Book 3 & 4*. Oxford University Press. Mussa, I. E. (2015). *Physics Made Simple for Secondary Schools*. Nyambari Nyangwine Publishers. National Examinations Council of Tanzania. (2010–2023). *NECTA O-Level Physics Past Papers*. Retrieved from https://www.necta.go.tz Anyakoha, M. W. (2002). *New School Physics for Senior Secondary Schools*. Africana-FEP Publishers. Nelkon, M., & Parker, P. (1995). *Advanced Level Physics*. Heinemann Educational Books.

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