How to find the experimental and actual length of the pendulum

What is a Simple Pendulum?

An ideal simple pendulum consists of a heavy point mass (called bob) tied to one end of a perfectly inextensible, flexible and weightless string. In practice, we make it by tying a metallic spherical bob to a fine cotton stitching thread.

Length of a Simple Pendulum

The distance between the point of suspension of the pendulum and its Centre of Gravity (C.G.), which is the C.G. of the bob, is called the length of the simple pendulum. It is represented using the aphabet ( l ).

Steps for finding length - 
 

1. Find the vernier constant and zero error of the vernier calipers and record it.
2. Determine the mean diameter of the simple pendulum bob using the vernier calipers.
3. Find the mean radius of the bob and represent it using ‘r’.
4. Attach a string to the bob. The length of the pendulum, l is adjusted by measuring a length of (l-r) from the top of the bob.
5. Put ink marks M1,M2 and M3 on the thread at distance of 50cm,60cm and 70cm from the C.G of the bob .
6. Pass the thread through the splited cork with the 50 cm mark at the bottom of the cork and tighten the two cork pieces between the clamp.
7. Fix the clamp in a stand kept on the table such that the height that the bob is just 2 cm above the laboratory floor.
8. Mark a point A on the floor just below the position of the bob at rest.
9. The equilibrium position of the pendulum is indicated by drawing a vertical line with a chalk on the edge of the table, just behind the string.
10. Find the least count and the zero error of the stop watch. Bring its hands to the zero position.
11. Move bob using the hand at an angle not more than 450 and leave it. See that the bob returns over the line without spinning.
12. The stop watch is started when the pendulum crosses the equilibrium position to any one side.
13. When it passes the equilibrium position in the same direction the next time it has completed one oscillation.
14. Just when the 20th oscillation is complete, count 20 and at once stop the stop watch.
15. Note the total time taken for twenty oscillations from the position of both the hands of the watch.
16. As we need two observations for the same length, repeat steps 12 to 15 one more time.
17. Repeat the experiment for lengths 60cm, 70cm, 80cm, 90 cm, 100cm, 110 cm, 120cm and 130cm.
18. In each case    is calculated. In all cases it is found that  is a constant.
19. The mean value of   is calculated and then the acceleration due to gravity is calculated using the relation 

To draw the l-T2 graph

The experiment is preformed as explained above. A graph is drawn with l along X axis and T2 along Y axis. The graph is a straight line, as shown in the figure.

To find the length of the second’s pendulum

A second’s pendulum is one for which the period of oscillation is 2 seconds. From the graph the length l corresponding to T2=4 s2 is determined. This gives the length of the second’s pendulum.

To find the length of the pendulum whose period is 1.5 seconds

The length l corresponding to T2 =1.52=2.25 is determined from the graph.

regards