# Investigation of relationship between period and length of a Simple Pendulum

When a pendulum swings through a small angle (about 7° or less) the time taken for one swing i.e. the periodic time, is given by the formula:
T = 2pi*sqrt(L/g) where L is the length of the pendulum and g is the acceleration due to gravity.

Procedure:
1. Press the Get Ruler button.

2. Measure and record the length of the pendulum.

3. Press the Start Swing button.

4. At a suitable position of the bob (eg left hand side), press Start Clock.

5. After 20 swings press the Stop Swing button. This will also stop the clock. Record the time for the 20 swings.

6. Press the Reduce Length button. The length is reduced by some random amount.

7. Repeat steps 1 to 6 at least six times.

8. Reset if necessary to get sufficient readings

Results:
Record the results in a table with headings as indicated here:

Length of pendulum(m) | Time for 20 swings(s) | Time (T) for 1 swing | T2

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 7 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
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