Simple Pendulum Lab

The Simple Pendulum Objective and Background Objective The Objective of this experiment is to witness the simple harmonic movement and to determine the value of the speedup repayable to sobriety from the analysis of the period of the simple pendulum. 1 Background There be three equations that will be employ to calculate the period of motion of the simple pendulum. They are the careen of the margin of the represent of T? against L, and the gravity of the pendulum motion.The period of the motion is the meter needed for one complete one shot that a pendulum bob swing from the initial position to the other end, and thence back to the initial position. 1 The equation to calculate period is, T = 2? Lg Where, T = Period of the motion, thrifty in s. L = Length of the pendulum, measured in cm. g = Acceleration callable(p) to gravity, measured in m/s2. The slope of the tie in the representical record of T? against L enkindle be used to determine the gravity of the pendulum mo tion. It is because, y = mx m = T? L= 4 g = Slope of the line in the graph T? /L. Therefore, to find the gravity of the pendulum motion, we can use the slope of the graph.The slope of the graph is give by the formula, g = 4 m g = Acceleration due to gravity, measured in m/s?. Procedure and Observations Materials * String * Metre Stick * S slide by watch * yield * Pendulum bob Procedure 1) Materials listed above were taken for the experiment. 2) The pendulum bob was tied tightly with the draw. 3) The string with the pendulum bob was hung on the stand. ) A meter stick was used to measure the distance between the centre of mass of the bob and the top of the string. 5) The distance was recorded in the observation table. 6) The pendulum ball was held at a distance from the centre and it was released. 8) A stop watch was used to time the time needed to complete ten cycles. 9) The time was recorded in the observation table. 10) Steps 4-7 were repeated four more(prenominal) times with antithetical lengths. Observations L (m) 10T (s) 0. 185 9. 01 0. 39 14. 13 0. 595 15. 04 0. 79 17. 58 1 19. 67Diagram of the Pendulum Figure 1 Calculations and Results Method 1 Graph of T2 vs. L Data collected L(m) T2(s2) 0. 18 0. 81 0. 39 1. 99 0. 59 2. 37 0. 79 3. 09 1 3. 86 Hand hurtlen graph ?x ?y Figure 2 The slope can be determined by m=? x? y. So, by taking a value for x x = 0. 4 cm y must(prenominal) then be y = 1. 4 cm m= 1. 4 cm0. 4 cm m=3. 5 The error would be given by ?mm= ? x1x12+ ? x2x22 ?m= m 0. 051. 42+ 0. 050. 42 ?m= 3. 5 0. 051. 42+ 0. 050. 42 ?m=0. 45 The acceleration due to gravity is given by g=4? 2m g=4? 23. 5 g=4? 23. 5 g=11. m/s2 calculative the error for g would yield ?gg= ? mm2 ?g= g 0. 453. 52 ?g= 11. 30. 453. 52 ?g= 1. 45 m/s2 g=11. 3 m/s2 1. 45 m/s2 answer for the percentage excursion would give % remainder= Actual value-Expected valueExpected value* nose candy% Expected value=9. 8 m/s2 % leaving= 11. 3 m/s2-9. 8 m/s29. 8 m/s2*100% % devia tion= 11. 3 m/s2-9. 8 m/s29. 8 m/s2*100% % deviation= 15. 3% Method 2 elongate Regression Excel graph Figure 3 The equation of the line is given by T2 = 3. 53L + 0. 33 Where m=3. 53 The acceleration due to gravity is given by =4? 2m g=4? 23. 53 g=4? 23. 53 g=11. 1 m/s2 Solving for the percentage deviation would give % deviation= Actual value-Expected valueExpected value* 100% Expected value=9. 8 m/s2 % deviation= 11. 1 m/s2-9. 8 m/s29. 8 m/s2*100% % deviation= 11. 1 m/s2-9. 8 m/s29. 8 m/s2*100% % deviation= 13. 2% Conclusion By comparing these 2 methods of shrewd the acceleration due to gravity it is clearly noticeable that at that place is a divergence between the two, when it comes to the accuracy. When calculating g using the hand drawn graph method it yielded =11. m/s2 1. 45 m/s2. However, when using the additive turnaround method on excel, it yielded g=11. 1 m/s2. This is clearly immediate to the expected value of 9. 8 m/s2. There are several(prenominal) reasons contr ibuting to the conclusion that additive regression is more accurate, than measuring calculating the slope off of a hand drawn graph. First of all, computing machines are much more accurate than adult male. There is no denying the fact that humans are not perfect and no hand drawn graph will be as precise as a computer drawn graph.A ruler was macrocosm used, which may lead to believe that the line is perfectly straight, whereas it is actually not. This is clearly noticeable when one zooms in on a hand drawn graph. Another problem with the ruler is that no matter how hard one tries to measure the distance between two different points, one will never be able to tie the exact distance. Computers however, Excel in this case, draw perfectly straight lines. as well as the location of line of best fit line, in the hand drawn part of the experiment, was estimated, which obviously leads to an inaccurate result.Excel however, uses the calculation of bilinear regression to draw the line of best fit and this is extremely accurate, since the exact slope is being calculated by Excel. It is clear that the method of linear regression is more accurate by looking at the percentage deviations for each method. The % deviation for the hand drawn graph yielded 15. 3%, whereas the percentage deviation for the linear regression method only was 13. 2% Even though the linear regression method was more accurate than the hand drawn method, there was still a pretty significant difference, between that value, namely g=11. m/s2, and the expected value of 9. 8 m/s2. This is due to a few sources of error when this experiment was conducted. One of the errors that contributed to this difference was that the length of the string was not exactly measured. Thus, the relation between the length and the period was wrong, leadership to false results. Another reason that contributed to the inaccuracy was the fact that when the bob was not vacillation the way it was supposed to. It was only sup posed to bewilder a linear motion, but it had a slight circular motion, which of course lead to a longer period.This again resulted in a wrong relation between the period and the length, leading to a wrong result. There was another major(ip) aspect to the experiment that lead to this result. Namely the fact one could not tell where the bob actually started its swinging motion exactly thereof the exact period could not be measured with the stopwatch. It is evident however, that if these errors could have been avoided, the acceleration due to gravity could have been calculated very accurately using the method of linear regression. References 1 PCS 125 Laboratory Manual, 2008