The swinging pendulum Mrs. Hanrahan’s precalculus class collected data on the length (in centimeters)

of a pendulum and the time (in seconds)

the pendulum took to complete one back-andforth swing (called its period). Here are their data:

Length (cm) Period (s)

16.5 0.777 17.5 0.839 19.5 0.912 22.5 0.878 28.5 1.004 31.5 1.087 34.5 1.129 37.5 1.111 43.5 1.290 46.5 1.371 106.5 2.115

(a) Make a reasonably accurate scatterplot of the data by hand, using length as the explanatory variable.

Describe what you see.

(b) The theoretical relationship between a pendulum’s length and its period is period =

2p

!g

"length where g is a constant representing the acceleration due to gravity (in this case, g = 980 cm/s2). Use the following graph to identify the transformation that was used to linearize the curved pattern in part (a).

(c) Use the following graph to identify the transformation that was used to linearize the curved pattern in part (a).

Transcribed Image Text:

2.2- 2.0- 1.8 1.6- 1.4- 1.2- 1.0- Period (s) 0.8- 0.6- 4 5 6 7 8 9 sqrt(length) 10 10 11