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Determination of the value of acceleration due to gravity(g) by a compound pendulum

Theory

Description
 

Table & Data Collection

Table-I

At the top Hole no. Distance from end in cm Time for 10 oscillations Time period in sec Mean time period, T (sec)
           
   1  10      
           
 E          
 N  2  20      
 D          
           
 A  3  30      
           
           
   4  40      
           
           
   1  60      
           
 E          
 N  2  70      
 D          
           
 B  3  80      
           
           
   4  90      
           

Calculations & Results

Calculation from grpah
 Length:
AC = C - A cm
BD = B - D cm

Mean Length:
L = (AC + BD) / 2 cm
 Corresponding time period from the graph:
T = from graph

g' = 4π² L / T² ms-2
(100 cm = 1 m)
 Error:
E = | g - g' ⁄ g | x 100%
Gravity = ms-2
Error = &

Discussion

Point Explanation
1 The comppund pendulum ws suspended from a rigid support.
2 The pendulum was slightly displaced from it's equilibrium position to start oscillation.
3 Small angular displacements were ensured so tht the motion approximates simple harmonic motion.
4 Time for 10 oscillations were taken from both ends with 8 holes with difference of 10 cm between each.
5 The time period and mean period were calculated.
6 A graph was drawn, distances in x-axis(10 small box = 10 cm) and mean time period in y-axis(first 10 = 1.5 afer 0.1 increase for 10 boxes) in table-I.
7 A line drawn that cuts between both lines twice with precise marks(T), and add points A,B,C and D. Now substract between CA and DB, then find mean length(L).
8 Find g' with formula 4𝜋2 ( L ⁄ T2 )
9 Calculate the error.
10 Errors occured due to air resistance, small errors in timing or imperfect alignment. Results were noted down.