this is the slide show of an experiment of acceleration due to gravity

1. Determining the acceleration due to gravity by applying linear least square regression method by using a simple
pendulum.

3. 1. Theory
We can determine the acceleration due to gravity by using a simple pendulum. At first,
we measure the length of the string and the time period of a simple pendulum. The
period of a simple pendulum is the time it takes to complete one oscillation. The period,
T, of a pendulum of length L is given by:
𝑇 = 2𝜋√ 𝐿 𝑔
After rearranging this equation, we get:
𝑇 2 = 4𝜋 2 𝑔 𝐿
After plotting the data onto a graph, we get a straight line. Therefore, comparing this with the straight line equation which is y=mx + c where m is the
slope of the line. We can determine the value of acceleration due to gravity by using the formula: 𝑔 = 4𝜋

5. 2. Apparatus
Metal bob
A piece of string
Meter scale
Clamp
Stand
Stop watch

6. 3. Procedure
A light piece of string is attached with the hook of the metal bob. The length L of the pendulum is measured using a
meter scale by holding it from the point of suspension to the center of the bob.
A small angle of about 10˚ is used to swing the pendulum. By measuring the total time for 20 oscillations and dividing
it by 20, the time period (T) is found. The procedure is then repeated for different lengths and the data is recorded in a
table.
The value of g for each set of data is calculated by using the values of L and T : g=4𝜋 2 ×
𝐿
𝑇2
The mean value of g and the standard deviation is calculated using equation.
To find the regression line, the Linear Least Square Regression Method (LLSRM) is used and from the value of slope, g
is found via the relation: slope=4π²/g.
A linear regression line of T² vs. L is plotted in excel.
 A comparison is done between the mean value of g and the value obtained by LLSRM with the reference value of
g by calculating the percentage of difference in each case. The variations (if any) are then discussed.

8. The mean value of g from the data: gM = 𝒈₁+𝒈₂+𝒈₃+𝒈₄+𝒈₅+𝒈₆+𝒈₇ 𝑵 = 1004.49 cm/ s2 =10.0449 cm/s2
Standard deviation: 𝜎 = 𝛫√ 1 𝑁 ∑(𝑔𝑖 − 𝑔Ϻ) 2 𝑁 𝑖=1 =.4.901 ms-2

9. The Percentage of difference between mean value and Reference value: % difference = gM−g 𝑔 × 100 = 2.34% The
Percentage of difference between LLSRM value and Reference value: (g= 9.81 m/s2 ) % difference = 𝑔𝐿−𝑔 𝑔 × 100 =
5.93%

10. 6. Discussion
 Measuring the time period of the pendulum’s oscillation can be challenging due to human reaction
time.
 Possible inaccuracies in measuring the length of the string attached to the bob.
 Inaccurate reading of the instrument
 The human error in starting a stopwatch and stopping a stopwatch could cause miscalculations
 The oscillations of the pendulum was affected due to the air resistance