Time period of a simple pendulum is directly proportional to the square root of its effective length.
T ∝ √l
Graph showing the variation of T2 with l is given below:
In order to find the acceleration due to gravity with the help of the above graph, we follow the following steps —
The slope of the straight line obtained in the T2 vs l graph, as shown in fig, can be obtained by taking two points P and Q on the straight line and drawing normals from these points on the X and Y axes. Then, note the value of T2, say T12 and T22 at a and b respectively, and also the value of l say l1 and l2 respectively at c and d.
Then,
Slope = PR\over QR = ab\over cd = T_1^2 - T_2^2\over l_1-l_2
This slope is found to be a constant at a place and,
Slope = 4 \pi ^2\over g
where, g = acceleration due to gravity at that place.
Thus, g can be determined at a place from the graph using the following relation,
g = 4 \pi ^2\over slope\ of\ T^2\ vs\ l\ graph