1. What is to be plotted? When the student is told to plot, say, S versus (vrs) t, it is accepted that this means: 1) S

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1. What is to be plotted?

When the student is told to plot, say, S versus (vrs) t, it is
accepted that this means: 1) S is the
dependent variable, plotted on the "y" or vertical axis; and, 2) t
is the independent variable, to be
plotted on the "x" or horizontal axis. This is a convention
(agreement) which should be memorised.

2. Choice of Scale.

The scale of a graph is the number of (usually) centimetres of
length of graph paper allotted to
a unit of the variable being plotted, for example 1cm for each 10
seconds of time. In general the
scales for the x and y axes may be different.
There are two criteria for choosing the scale of a graph, range of
the variable, and convenience
in plotting:

a) Range of the variable: Suppose the range of values of S is from
5 cm to 125 cm. We then need
a scale for S that allows us to plot values from 0 to values
somewhat greater than 125 cm. Notice
that (unless told to do so by the instructor) we do not choose to
suppress the zero of the graph and
start the S scale from 5 cm. The reason is that we may later need
to use the graph to find values
extrapolated (continued) to the zero.
Also we usually try to allow space on the graph for values somewhat
greater than the largest
value (in this example, 125 cm) because we may take a little more
data in the experiment, with larger
values, or we might want to extrapolate the graph to larger
values.
Finally the scale should be chosen to most nearly use the whole of
the graph paper. Just
because a choice of, say, l cm to represent 1 sec of time makes the
graph easy to plot, we should
not do this if it makes the graph only occupy a small part of the
whole paper and be hard to read and
use.

b) Convenience in Plotting: It turns out (as we shall see in an
exercise in this lab) that scales of 1,
2, 5, and 10 (and multiples of 10 of these) per centimetre are
easiest to use; a scale of 4 per
centimetre is somewhat more difficult, but can be used; but scales
of 3, 6, 7, 9, etc., per centimeter
are very difficult and should be avoided.
In choosing scales it sometimes helps to turn the paper so that the
"x-axis" is either the long or short
dimension of the paper.

3. Label the Axes and put a title to the graph

The vertical and horizontal axes of the paper should carry labels
of the quantities to be plotted,
with units. In our previous example the label on the y-axis would
be: S (cm). The graph itself should
have a title. In our example the title is: Plot of S vs. T.
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4. Circle your Data Points

Each data point should have a neat circle drawn around it. If more
than one experimental trial
is used one can use circles, triangles, squares, with a legend to
distinguish these.

5. Put a Smooth Solid Curve through the Data Points

This can be done "by hand" or with a plotting aid. Ignore any
points that fall far outside the
curve (after checking that they are plotted correctly). A dashed
line should indicate extrapolations
to larger or smaller values, outside of the range of data
taken.

6. Graphical Analysis

Often we have data (x, y) which we believe follows the theoretical
relation y = rnx + b; we can
verify this relation if we obtain a straight line when we plot y
vrs x. Also, the plot obtained allows us
to find the values of m and b as follows:
b = y-intercept of graph (value of y when x = 0) m = slope of graph
= y/x = (Y2-Y1)/(X2-X1 )


Figure 1: Graph X vs Y

Other times we have data that we believe follows a non-linear
theoretical relation. For example
consider S = (1/2)* aT². We can verify this relation by plotting S
vrs T². If this relationship holds then
the graph will be a straight line with intercept zero. The slope of
the graph then gives the constant
a/2.

Remarks: The points chosen to determine the slope should be
relatively far apart. Points
corresponding to data points should not be chosen, even if they
appear to lie on the line.


Y (units)
X (units)
(x1, y1)
(x2, y2)
x
y
Y-INTERCEPT
y = mx + b
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EXPERIMENTAL PROCEDURE

Exercise 1:

Consider the following data:

Table 1: Position & Time
S (m) 0.27 1.08 2.43 4.32 6.75 9.72
T(sec) 0.10 0.20 0.30 0.40 0.50 0.60

 On a sheet of graph paper draw 5 lines parallel to the y-axis,
each separated by a few
centimetres. Plot the values of S on the 5 lines to the following
scales (with some scales you
may not be able to plot all points):

a) 1 m equivalent to 1cm.
b) 1 m equivalent to 2cm.
c) 1 m equivalent to 3cm.
d) 1 m equivalent to 5cm.
e) 1 m equivalent to 7cm.

 Which scales are easy to plot?
 Which scales are difficult? Explain why.

Exercise 2:

 Plot a graph of S Vs T.
 Does this plot give a straight line?

Exercise 3:

 On the same graph paper as for exercise 2, plot a graph of S vrs.
T². This should give a
straight-line plot.
 What is the y-intercept of this graph?
 What is the slope of the straight line? (Include units.)

Conclusion:
Conclusions are a necessary part of every experiment. The main
purpose of the conclusions
is to summarise the following: