Simple Pendulum Lab Manual

1. Title: Simple Pendulum Lab

2. Objective:

3. Introduction:

A simple pendulum consists of a point mass suspended from a fixed point by a massless string or rod. When the pendulum is displaced from its equilibrium position and released, it oscillates back and forth due to the force of gravity.

The period (T) of a simple pendulum, which is the time it takes for one complete oscillation, is given by the following formula:

T = 2π * sqrt(L / g)

where:

This formula is valid for small angles of displacement (typically less than 15 degrees). In this lab, you will investigate the relationship between the period of a simple pendulum and its length and determine the acceleration due to gravity.

4. Materials:

5. Procedure:

1. Setting up the Simple Pendulum:

  1. Attach the string or thread to the support stand.
  2. Attach the small mass to the other end of the string or thread.
  3. Measure the length of the pendulum (L) from the fixed point to the center of the mass. Record the length in a table.

2. Measuring the Period of the Pendulum:

  1. Displace the pendulum from its equilibrium position by a small angle (e.g., 10 degrees).
  2. Release the pendulum and allow it to oscillate.
  3. Use the stopwatch to measure the time it takes for the pendulum to complete 10 oscillations. Record the time in a table.
  4. Repeat the measurement several times for the same length.
  5. Repeat the experiment with different lengths of the pendulum.

6. Data Analysis:

Calculate the period (T) of the pendulum for each length by dividing the total time for 10 oscillations by 10. Calculate the average period for each length. Plot a graph of T² vs. L. The slope of the graph should be equal to 4π²/g. Determine the acceleration due to gravity (g) from the slope of the graph. Estimate the uncertainties in your measurements and propagate them to calculate the uncertainties in your g value. Compare your result with the accepted value of g (9.81 m/s²) and discuss any discrepancies.

7. Discussion:

  1. How does the period of the pendulum depend on its length?
  2. How does the period of the pendulum depend on the mass of the bob?
  3. How does the period of the pendulum depend on the initial angle of displacement?
  4. Discuss the sources of error in your measurements. How could these errors be minimized?
  5. How well does your experimental result for g agree with the accepted value?
  6. What are some practical applications of simple pendulums?

8. Conclusion:

In this lab, you have investigated the relationship between the period of a simple pendulum and its length and determined the acceleration due to gravity (g) using a simple pendulum. You have also learned how to analyze the motion of a simple pendulum using the small-angle approximation. By understanding the factors that affect the period of a simple pendulum, you have gained a deeper understanding of the principles of oscillatory motion.