To investigate the relationship between the period
and length of a simple pendulum, hence measure g
Background:
When a pendulum swings through a small angle (about 5° or less) the
time taken for one swing i.e. the periodic time, is given by the formula:
where L is the length of the pendulum and g is the acceleration
due to gravity.
Procedure:
Press the Start swing button to make the pendulum swing
At a suitable position of the bob (eg left hand side), press Start
clock
After 20 swings press the Stop clock button. Record the time for
the 20 swings
Press the Stop swing button
Press the Get ruler button
Measure and record the length of the pendulum
Press the Reduce Length button. The length is reduced by some random
amount.
Repeat steps 1 to 7 six times. Press Reset if necessary
Results:
Record the results in a table with headings as indicated below.
Length of pendulum (m) Time for 20 swings (T20(s))
Time for 1 swing (T(s)) T squared
Graph:
Plot a graph (on graph paper) of L (y-axis) against T². Note:
Start both axes at zero. A straight line graph through the origin shows
that length is proportional to periodic time squared. Note: The
slope of the line is L / T²
Calculations:
From the graph, pick two suitable points (far apart) to calculate the
slope of the line. The value of g is calculated using the formula: g =
4(pi)²(slope)
Precautions:
Ensure that your eye
is level with the centre of the bob when measuring length to avoid
parallax error
Use a split cork to hold
the string (keeps length constant and is easy to measure from bottom
of cork to centre of bob)
Do not cause the pendulum
to swing through an angle greater than 5 degrees approx.
Ensure that the pendulum
swings in one plane only - avoid circular movements
Use a long pendulum as much as possible to keep measurement errors
(length and time) relatively small