A pendulum period investigation is a classic school project because it connects a simple classroom setup to a powerful mathematical model. By timing how long a hanging mass takes to swing back and forth, students can test which variables affect the motion. The main goal is to see how the period changes when length, mass, and starting angle are adjusted.
This experiment builds skills in measurement, graphing, controlled variables, and interpreting real data.
For small angles, a simple pendulum follows the equation T = 2*pi*sqrt(L/g), where T is the period, L is the pendulum length, and g is gravitational acceleration. This model predicts that period depends on length, not on the mass of the bob, and only weakly on amplitude if the angle is small. A useful graph is period T versus sqrt(L), which should form a straight line if the model is correct.
From the slope of that line, students can estimate g and evaluate experimental error.
Key Facts
- Pendulum period is the time for one complete back-and-forth swing.
- For small angles, T = 2*pi*sqrt(L/g).
- Period increases as length increases because T is proportional to sqrt(L).
- Changing the bob mass should not change the period of an ideal simple pendulum.
- Keep the starting angle small, usually less than about 15 degrees, to use the simple pendulum formula.
- A graph of T versus sqrt(L) should be linear with slope 2*pi/sqrt(g).
Vocabulary
- Period
- The time required for one complete cycle of motion, such as one full swing of a pendulum.
- Length
- The distance from the pivot point to the center of mass of the pendulum bob.
- Amplitude
- The maximum displacement from the equilibrium position, often measured as the starting angle for a pendulum.
- Controlled variable
- A factor kept the same during an experiment so that the effect of one chosen variable can be tested.
- Linear graph
- A graph whose data points follow a straight-line pattern, showing a constant rate of change between the plotted variables.
Common Mistakes to Avoid
- Measuring length to the bottom of the bob, not its center, gives a length that is too large and makes the calculated period comparison inaccurate.
- Timing only one swing makes reaction time error very large, so students should time many swings and divide by the number of swings.
- Changing length, mass, and amplitude at the same time prevents a fair test because the effect of each variable cannot be separated.
- Using a large starting angle while applying T = 2*pi*sqrt(L/g) is wrong because the simple formula assumes small-angle motion.
Practice Questions
- 1 A pendulum has length L = 0.80 m. Using g = 9.8 m/s^2, calculate its predicted period using T = 2*pi*sqrt(L/g).
- 2 A student times 20 complete swings of a pendulum and records 36.0 s. What is the period of one swing, and how does it compare to a predicted period of 1.79 s?
- 3 In an experiment, changing the bob from 50 g to 200 g gives nearly the same period, but increasing the length gives a larger period. Explain why this result supports the simple pendulum model.