# Harmonic Motion - Deriving the Formula for a Pendululm

Determine the formula for the period of a pendulum. The period is defined as the time required for a complete out-and-back swing.

Measuring the period: The easiest way to measure the period accurately is to measure the time for a large number of swings and divide by this number to determine the time required for one complete swing. In this investigation, measure the time for ten complete swings and divide by ten to determine the period of the pendulum (a single swing).

Measuring the length of the pendulum: Measure the length from the pivot point to the center of mass of the paperclip / washer assembly.

Investigate

• Period as a function of mass. Keep the length constant while varying the mass.
• Period as a function of length. Keep the mass constant while varying the length.
• Enter your data in the form below. Make certain to enter in the correct category (constant mass or constant length). Repeat for each measurement. Please note, you will only add information in one category at a time (constant mass OR constant length).

Questions

• What effect does the mass have on the period of the pendulum?
• What effect does the length have on the period of the pendulum?
• Based upon your observations, develop a formula to determine period as a function of mass and length.

## Analysis:

Analyze the Data

• Develop a graph of Period vs. Mass. What effect does the mass have on the period of the pendulum?
• Develop a graph of Period vs. Length. What effect does the length have on the period of the pendulum?
• Based upon your observations, develop a formula to determine period as a function of mass and length.