MATHEMATICAL PENDULUM

MATHEMATICAL PENDULUM

Aim
This experiment was performed to determine the gravitational acceleration of objects close to the surface of the earth, by observing the motion of a simple pendulum.

Introduction
A simple pendulum is one which can be considered to be a point mass suspended from a string or rod of negligible mass
For oscillations where the angle  is small, the period T is related to the length L of the string and the gravitation constant g by
T = 2π√(l/g)
Squaring both sides of this equation yields
T2 = 4π^(2 ) l⁄g so, g = (4π^(2 ) l)/T^2
(Giancoli, 2001:376)
Equipment and material
Rope
Stative
Pendulum
Stopwatch
Ruler bow degree of active stroke

Experimental Method
Preparing materials and appliance to be used
Stringing up materials and appliance like [at] picture
Measuring string length equal to 30cm
Diverting string which have been given by pendulum as far as 100
Calculating time required to do 10 times oscillation
Noting result of attempt into tables of perception
Repeating step 3-6 with different string length

Data Tabulation
No. String length(m) Jumlah osilasi Time for 20 oscillations Time T for one
oscillation (s) Period
squared (s2)
Data Analysis
T = 2π√(l/g)
T2 = 4π^(2 ) l⁄g
g = (4π^(2 ) l)/T^2

1.a. l= 0.2 m g = (4π^(2 ) l)/T^2
T= 0.98s = (4〖(3.14)〗^(2 ) 0.2)/0.9604
= 8.2129 ms-2
Discussion
Mathematical pendulum experiment was titled. This experiment was performed to determine the gravitational acceleration of objects close to the surface of the earth, by Observing the motion of a simple pendulum. The tools and materials used are rope, stative, pendulum, stopwatch, ruler degree of active bow stroke. The steps undertaken in conducting this experiment is the first Preparing materials and appliances to be Used, stringing up materials and appliances like this picture:

Next, measuring string length is equal to 0.2 m, diverting the string the which have been given by the pendulum as far as 100 , it is to avoid twisting. According to the theory stated that the ideal angle is used to perform an experiment determining the magnitude of gravity is less than 150 (Giancoli, 2001: 375-376). The next step is calculating time required to do 20 times Oscillation, then Noting result of attempt into tables of perception, to 20cm long rope showed that the average time was 19.63 seconds. Next to a long string of 0.25 m, the time required for oscillation is 20 times 21.47sekon. To 0.3 m long string, the time required for oscillation is 20 times 22.8sekon. For the length of rope 0:35 m, the time required for oscillation is 20 times 24.58sekon. To 0.4 m long string, the time required for oscillation is 20 times 26.26sekon.
After conducting the experiment and the data obtained, praktikan perform calculations to determine the value of the acceleration of gravity. The amount of gravitational acceleration is calculated by the equation:
g = (4π^(2 ) l)/T^2
For a long string of 0.2m gravitational acceleration is obtained by an average of 8.1852ms-2. Next to a long string of 0.25m gravitational acceleration is obtained by an average of 8.5608ms-2. For a long string of 0.3M gravitational acceleration is obtained by an average of 9.1044ms-2. For a long string of 0.35m gravitational acceleration is obtained by an average of 9.1392ms-2. For a long string of 0.4m gravitational acceleration is obtained by an average of 9.1492ms-2. Based on the results of the acceleration of gravity is above average in mind that the results of the experiment less in accordance with existing theory, which states that the magnitude of gravity is 9.8ms-2(Halliday, D., Resnick, R., and Walker, J, 1993). The discrepancy may be due to several factors: the influence of wind, less careful praktikan in calculating the period of 20 times the oscillation and measuring the angles of oscillation.
When depicted in the graph, the relationship T2 and g are as follows:

Based on the above chart can be seen that the longer the string (l) then, the magnitude of the square of its period (T2). This is in accordance with the theory that the relationship between l and T2 is directly proportional.

Conclusion
By means of a simple pendulum, the value of the gravitation constant was determined to be l=0.2m; g= 8.1852m/s2, l=0.25m; g= 8.5608m/s2, l=0.30m; g= 9.1044m/s2, l=0.35m; g= 9.1392m/s2, l=0.40m; g= 9.1492m/s2. This agreed with the accepted value, 9.8 m/s2.