The period of a pendulum is the time required for one oscillation; the pendulum is usually referred to as simple when the angle made with the vertical is less than 5°. An experiment is conducted in which simple pendulums are constructed with different lengths, and the corresponding periods are recorded. The following data are collected. Physics theory states that the period of a simple pendulum is related to the length of the pendulum through a power equation.

(a) Draw a scatter diagram treating length as the explanatory variable.

(b) Determine the logarithm of both the x- and y-values so that X = log x and Y = log y. Draw a scatter diagram of the transformed data.

(c) Find the least-squares regression line of the transformed data.

(d) Find the power equation of best fit.

(e) Use the power equation of best fit to predict the period of a simple pendulum whose length is 2.3 feet.

Transcribed Image Text:

Length (feet),.x Period (seconds), y 1 1.10 2 1.55 3 1.89 4 2.24 5 2.51 6 2.76 7 2.91