Simple Pendulum Lab
The Simple Alarm Objective and Background Objective: The Objective of this agreement is to appraise the simple harmonic motion and to actuate the amount of the dispatch due to force from the assay of the aeon of the simple pendulum.  Background: There are three equations that will be acclimated to account the aeon of motion of the simple pendulum. They are the abruptness of the band of the blueprint of T? adjoin L, and the force of the alarm motion.
The aeon of the motion is the time bare for one complete aeon that a alarm bob beat from the antecedent position to the alternative end, and afresh aback to the antecedent position.  The blueprint to account aeon is, T = 2? Lg Where, T = Aeon of the motion, abstinent in s. L = Breadth of the pendulum, abstinent in cm. g = Dispatch due to gravity, abstinent in m/s2. The abruptness of the band in the blueprint of T? adjoin L can be acclimated to actuate the force of the alarm motion. It is because, y = mx m = T? L= 4?? g = Abruptness of the band in the blueprint T? /L. Therefore, to acquisition the force of the alarm motion, we can use the abruptness of the graph.
The abruptness of the blueprint is accustomed by the formula, g = 4?? m g = Dispatch due to gravity, abstinent in m/s?. Procedure and Observations Materials: * Cord * Metre Stick * Stop watch * Angle * Alarm bob Procedure: 1) Materials listed aloft were taken for the experiment. 2) The alarm bob was angry deeply with the string. 3) The cord with the alarm bob was afraid on the stand. ) A beat stick was acclimated to admeasurement the ambit amid the centre of accumulation of the bob and the top of the string. 5) The ambit was recorded in the ascertainment table. 6) The alarm brawl was captivated at a ambit from the centre and it was released. 8) A stop watch was acclimated to time the time bare to complete ten cycles. 9) The time was recorded in the ascertainment table. 10) Steps 4-7 were afresh four added times with altered lengths. Observations: L (m)| 10T (s)| 0. 185| 9. 01| 0. 39| 14. 13| 0. 595| 15. 04| 0. 79| 17. 58| 1| 19. 67|
Diagram of the Alarm Figure [ 1 ] Calculations and After-effects Adjustment 1 – Blueprint of T2 vs. L Data calm L(m)| T2(s2)| 0. 18| 0. 81| 0. 39| 1. 99| 0. 59| 2. 37| 0. 79| 3. 09| 1| 3. 86| Duke fatigued blueprint ?x ?y Figure [ 2 ] The abruptness can be bent by m=? x? y. So, by demography a amount for x x = 0. 4 cm y charge afresh be y = 1. 4 cm m= 1. 4 cm0. 4 cm m=3. 5 The absurdity would be accustomed 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 dispatch due to force is accustomed by g=4? 2m g=4? 23. 5 g=4? 23. 5 g=11. m/s2 Artful the absurdity for g would crop ?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 Solving for the allotment aberration would accord % deviation= Actual value-Expected valueExpected value* 100% Accepted value=9. 8 m/s2 % deviation= 11. 3 m/s2-9. 8 m/s29. 8 m/s2*100% % deviation= 11. 3 m/s2-9. 8 m/s29. 8 m/s2*100% % deviation= 15. 3% Adjustment 2 – Beeline Corruption Excel blueprint Figure [ 3 ]
The blueprint of the band is accustomed by T2 = 3. 53L + 0. 33 Area m=3. 53 The dispatch due to force is accustomed by =4? 2m g=4? 23. 53 g=4? 23. 53 g=11. 1 m/s2 Solving for the allotment aberration would accord % deviation= Actual value-Expected valueExpected value* 100% Accepted 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% Cessation By comparing these two methods of artful the dispatch due to force it is acutely apparent that there is a aberration amid the two, back it comes to the accuracy. Back artful g application the duke fatigued blueprint adjustment it yielded =11. m/s2 ± 1. 45 m/s2. However, back application the beeline corruption adjustment on excel, it yielded g=11. 1 m/s2. This is acutely afterpiece to the accepted amount of 9. 8 m/s2. There are several affidavit accidental to the cessation that beeline corruption is added accurate, than barometer artful the abruptness off of a duke fatigued graph. First of all, computers are abundant added authentic than humans. There is no abstinent the actuality that bodies are not absolute and no duke fatigued blueprint will be as absolute as a computer fatigued graph.
A adjudicator was actuality used, which may advance to accept that the band is altogether straight, admitting it is absolutely not. This is acutely apparent back one zooms in on a duke fatigued graph. Addition botheration with the adjudicator is that no amount how adamantine one tries to admeasurement the ambit amid two altered points, one will never be able to get the exact distance. Computers however, Excel in this case, draw altogether beeline lines. Also the area of band of best fit line, in the duke fatigued allotment of the experiment, was estimated, which acutely leads to an inaccurate result.
Excel however, uses the adding of beeline corruption to draw the band of best fit and this is acutely accurate, back the exact abruptness is actuality affected by Excel. It is bright that the adjustment of beeline corruption is added authentic by attractive at the allotment deviations for anniversary method. The % aberration for the duke fatigued blueprint yielded 15. 3%, admitting the allotment aberration for the beeline corruption adjustment alone was 13. 2% Even admitting the beeline corruption adjustment was added authentic than the duke fatigued method, there was still a appealing cogent difference, amid that value, namely g=11. m/s2, and the accepted amount of 9. 8 m/s2. This is due to a few sources of absurdity back this agreement was conducted. One of the errors that contributed to this aberration was that the breadth of the cord was not absolutely measured. Thus, the affiliation amid the breadth and the aeon was wrong, arch to apocryphal results. Addition acumen that contributed to the blunder was the actuality that back the bob was not accepted the way it was declared to. It was alone declared to accept a beeline motion, but it had a slight annular motion, which of advance advance to a best period.
This afresh resulted in a amiss affiliation amid the aeon and the length, arch to a amiss result. There was addition above aspect to the agreement that advance to this result. Namely the actuality one could not acquaint area the bob absolutely started its accepted motion exactly; accordingly the exact aeon could not be abstinent with the stopwatch. It is axiomatic however, that if these errors could accept been avoided, the dispatch due to force could accept been affected actual accurately application the adjustment of beeline regression. References  PCS 125 Laboratory Manual, 2008
Order a unique copy of this paper