The document summarizes an experiment that tested how different factors affect the period of a pendulum. It was found that increasing the length of the string increased the period, as a longer string requires a greater distance to travel. The period was also unaffected by the mass of the bob or the angle of displacement. The only minor variations observed were attributed to random error and reaction times in taking measurements.

1. It was shownthatthe lengthof the stringaffectedthe periodof a pendulum.Thiswas
displayedinthe resultsasthe differenttimestakenfor20 oscillationswhilstchangingthe lengthof the
stringvariedfrom12.60 to 30.90 seconds.Meanwhile the timescalculatedforone oscillationvaried
from0.63 to 1.54 seconds. Here the reasoningbehindthisfinding. Anobjectona pendulumwithalong
stringisfurtheraway fromthe axisof the pendulum.Thismeansthatithasto covera longerdistance to
returnto where itcame from.Thisisthe case since a longerradiusfromthe axisof rotationmeansa
longerarc lengthforthe bob to travel along. The formulalinkingthe lengthof the stringtothe periodof
the pendulumisseenbelow:
𝑇 = 2𝜋√𝑙
𝑔
Where ‘T’ isthe period,‘l’isthe lengthof the stringand ‘g’is the gravitational fieldstrength.
The mass of the bobdoesn’taffectthe periodof the pendulumsince the movementisdue to
gravity.Accelerationdue togravityisaconstant figure( 9.8ms-2
) and no matterhow heavythe bobis,
the pendulumwillaccelerateatthisrate and take the same amountof time tocomplete one backand
fro movement.Asshowninthe experiment,the time takenfor20 oscillationsonlyvariedfrom24.10 to
25.18 seconds.Thisvariationinthe resultsisonlytodue the randomerror and the vary reactiontimes
to measure the oscillations.The timescalculatedforone oscillationwithvaryingmassesalsohada small
range from 1.21 to 1.26 seconds.
Finallythe angle of displacementwastestedandresultsshowedthatthisfactordoesn’treally
affectthe periodof a pendulum.Timesfor20 oscillationsrecordedatdifferentanglesvariedonlyfrom
21.65 to 22.65 secondswhilstthe time calculatedforone oscillationrange from1.08 to only1.13
seconds.Whenthe angle of displacementincreases,the startingheightof the bobishigherthusitwill
accelerate overa longerperiodandgaina greatervelocity.However,thismovementisoveralonger
distance,sothe time takenforone oscillationwill notdecrease.Itwill remainconstant.
It was advisable todivide the resultsby20 to reduce randomerror due to humanreactiontime.
Sources of Error
Sourcesof Error:
- The time for one oscillationwasslightlyinaccurateasfriction due toair resistance slowsthe
pendulumdownwitheachswing.
- There wasuncertaintyinthe reference pointatwhichtostart and the stopthe watch.

2. Precautions
- The time takenfor 20 oscillationswasdividedby20 to reduce the error due to human
reactiontime.
- All windowswere closedtoensure thatthe force of the winddidnot affectthe movement
of the pendulum.