When the program starts, it automatically collects data for a pendulum of given length.
Heading: Collecting data
Obtain points on the graph for several values of L, ranging from small to large.
Heading: Analysing your data.
Choose the item "Analyse data" on the menu.
From your graph of T vs L, you see that the points do not lie on a straight line through the origin. The equation relating T to L is a power law:
Sprite: sp2 : T=aL(n)
An equation of this type can be made into a linear equation by taking logarithms of both sides:
Sprite: sp3 logT = loga + logL
This shows that the graph of y=(log T) vs x=(log L) is a straight line with gradient n.
Choose "Log-log graph" on the menu. The computer draws the log-log graph, and finds the best values for n and a from your data. It also gives the result for g, the acceleration of gravity.
Heading: Results and Conclusions.
Dynamics shows that the period T of a pendulum of length L is:
Sprite: sp1 T=2(pi) root L/g
Comparing this equation with
Sprite: sp2 T=aL(n)
you see that
Sprite: sp4 n=1/2 and a=2pi/rootg
Your measured value of n is consistent with 1/2, taking into account the standard deviation of your result.
The second equation can be used to find g:
Sprite: sp5 g=4pi^2/a^2
Your value, with its standard deviation, is again consistent with the usual value
Sprite: sp6 REM g=9.81ms(-2)
Heading: Comments
The Simple Pendulum is not the only way of measuring g. It is slow, and not very accurate.
The experiment described in this package is not the best way of using a simple pendulum. Instead of measuring the time for each swing, it is much better to measure the time for, say, 20 swings, and divide by 20.
The error e in timing 20 swings is the same as the error in measuring one swing, and so the error in your estimate of the period is e/20
