A Pendulum

Instructions

Attach a hanging mass (>15 grams) to a string to make a pendulum. Attach the pendulum to a support with the center of the hanging mass 5 cm below the pivot point.

Pull the mass aside and release it. Use a stop watch to determine the time required for 10 complete cycles. Divide the total time by 10 to calculate and record the time for one cycle (called the period). Repeat in 5 cm increments up to a length of 50 cm. Be sure to record the length and period for each trial.

Analysis

  1. Clear any existing lists from your TI-8X and enter the periods in list L1 and the string lengths in list L2.
  2. Construct a scatter plot of string length versus period for your data with period on the y-axis.
  3. Perform a linear regression (LinReg) analysis, identifying the regression equation using the given formula, y=ax+b. Note the regression equation and correlation coefficient.
  4. Perform a power regression (PwrReg), identifying the regression equation using the given formula, y=ax^b. Note the regression equation and correlation coefficient.
  5. Determine which regression "best fits" the data and write a mathematical expression relating string length and period for the pendulum.

Instructions #2

  1. Repeat the pedulum experiment for lengths of 50 and 100 cm. Add the data to L1 and L2.
  2. Perform the regression analysis again (linear/power) to determine if the initial relationship holds true for longer pendulums.

Questions

  1. Use the equation Equation to solve for g which is the acceleration due to gravity. Be sure to record your units.
  2. The accleration due to gravity is an accepted physical constant (9.8 m/sec^2). Use g = 9.8 m/sec^2 to solve for Pi Symbol . How does the value compare to the excepted value of 3.14?
  3. For a power regression (period = 0.20*length^0.5), what is the significance of length raised to the 0.5 power?