Question

A pendulum is connected to a rubber band which is in turn being oscillated by a small electric motor. A student, Leilani, measures the period of time T taken for the pendulum to swing, repeating for 8 different lengths L of the pendulum. She tries to plot T against L but the graph is not linear. Her teacher suggests plotting T2 against L instead. Leilani's results are shown in the graph below. You may assume that all the data is valid. Leilani used her pendulum data graph to obtain the gradient using a manual graphical method. The maximum limits on the axes that Leilani used are Y = 14 s2 on the y-axis and X = 2 m on the x-axis Use a manual graphical method to estimate the gradient of the line of best fit for Leilani's graph in s2 m-1

Answer 1

Number of divisions on x axis = 10

each sub unit = max value/10 = 2/10 = 0.2m

Number of divisions on y axis = 10

Each sub unit = max value/10 = 14/10 = 1.4 s²

Draw a line that best fits the given points, by trying to keep equal amounts of points above the line as below.

To find the gradient,

x = 1 sub unit = 0.2m

y = 4/5 of a sub unit = (4/5) x 1.4 = 1.12s²

Gradient =y/x = 1.12/0.2 = 5.6 s²/m