Difficult# Pendulum Equation Constant

SATPHY-NMCZY1

The equation for the period of a pendulum is:

$$ T\ =\ 2\pi \sqrt { \frac { L }{ g } } $$

Three students in a lab group gather data for a pendulum as they vary its length and measure the period for each length. From the data, they construct the graph pictured below, where they plot period ($T$) on the vertical axis (in seconds) and the square root of length ($ \sqrt { L } $) on the horizontal axis (in "square root of meters").

From the graph, what value do the students obtain for the constant that should be $2 \pi?$:

$$( g = 9.8\ { m }/{ { s }^{ 2 } } )$$