Tru Physics

Simple Pendulum

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[This experiment can be completed easily at home without specialized equipment.]

Simple Pendulum. Note that the time it takes to go from the left to the right side and then back to the original position on the left is defined as the pendulum's period.
Simple Pendulum. Note that the time it takes to go from the left to the right side and then back to the original position on the left is defined as the pendulum’s period.

The purpose of this lab is to determine how a pendulum’s mass affects the period of its swing. Furthermore, we wish to determine an experimental value for the acceleration due to gravity and compare that to the known value of 9.81 \frac{m}{s^2}.

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Materials:

Procedure:

  1. Tie one of the masses to the end of the string or thread.
  2. Secure the other end of the string to a stationary object. (For example, a closet clothing rod).
  3. Swing the pendulum mass back and forth in a small arc by pulling it to the side once and then releasing. Have someone hold a protactor up to the top of the pendulum so that the release angle can be measured. You will want to use the same angle for all five masses. Be sure that the protractor does not interfere with the swinging of the pendulum.
  4. Measure the time it takes for the pendulum to make ten complete swings. Record this time as the period.

Note: For best results, conduct the experiment in a room with minimal air movement to minimize any external disturbances on the swinging motion of the pendulum.

  1. Repeat steps 1-4 for five different masses total, using the second object to vary the mass of the pendulum. Be sure to keep the length of the string and the angle of the swing constant.
  2. Calculate the average period (the time it takes for the mass to return to its original location) for each mass and record your results.

T_{AVG} = \dfrac{t_{total}}{N_{swings}}

where:

  • T_{AVG} is the average period of the pendulum,
  • t_{total} is the total time it takes for the pendulum to make ten complete swings, and
  • N_{swings} is the total number of swings, so N=10.
  1. Plot a graph of the period against the mass of the pendulum (Logger Pro is a great tool to use for this). Analyze your results and draw a conclusion. Period will be your y-axis (vertical) variable and mass will be on the x-axis (horizontal).
  2. Using the average period and length of the pendulum, calculate the gravitational acceleration (g) at the location where the experiment was conducted. Use the formula T_{AVG}=2 \pi \sqrt{L/g} to do this. Note: you will need to use algebra to solve for g.

Metric System: In physics, we rely strongly on the metric system. Although it is less common in the US, it simplifies the math significantly. So, you will want to measure the length of the pendulum string in meters in order for your calculations to be correct. Remember that 100 cm are in 1 meter. So, if you measure the length to be 18.5 cm, you would move the decimal point over two places to the left for a value of 0.185 meters.

  1. Now compute the percent error between the value you obtained in step 8 and the known value of g which is given as g=9.81 \frac{m}{s^2}. Use the formula below:

\% Error = \dfrac{|g_{measured}-g_{theoretical}|}{g_{theoretical}}

where:

  • || are absolute value bars. Note that %Error is never negative because of this.
  • g_{measured} is the value for g that was obtained in step 8 through the experimental process.
  • g_{theoretical} is the known value of g, 9.81 \frac{m}{s^2}.

We generally accept percent errors less than 10%. If care is taken, this lab can be completed with a percent error of less than 5%.

Future Research: You can use different objects of the same mass and instead vary the length of string to investigate how this factor affects the period of a pendulum as well.

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