This experiment investigated factors that affect the period of a pendulum. It was found that the length of the string affected the period, with longer strings resulting in longer periods. Specifically, doubling the length of the string doubled the period. The mass of the pendulum did not affect the period. Finally, the angle of the pendulum swing was found to not significantly impact the period either.

1. Thisexperimentwascarriedoutto investigatethe factorsthataffectthe periodof a pendulum.
A pendulumisaweighthungfroma fixedpointsothatitcan swingfreely. The total energythroughout
the movementof the pendulumremainsconstant.Atitshighestpoint,ithasitsmaximumpotential
energyandno kineticenergy.Asitbeginstofall,the potential energybeginstochange intokinetic
energyuntil itreachesits lowestpointwhere the kineticenergyisata maximumandthe potential
energyisequal tozero.Whenit beginstorise againthe kineticenergybeginstochange potential energy
until itreachesitsmaximumonce againat the highestpoint.
A pendulummovesbackandfro due to gravity. Whenthe massis drawnupwardsand letgo,the
force of gravityacceleratesitbackto the original position.The momentumbuiltupbythe acceleration
of gravitycausesthe massto thenswinginthe opposite direction to aheightequal tothe original
position. Thisforce iscalledinertia:(itstendencytoresistitsstate of motion.)
It was shownthatthe lengthof the stringaffectedthe periodof a pendulum.Thiswasdisplayed
inthe resultsasthe differenttimestaken for20 oscillationswhilstchangingthe lengthof the string
variedfrom12.60 to 30.90 seconds.Meanwhile the timescalculatedforone oscillationvariedfrom0.63
to 1.54 seconds. Here the reasoningbehindthisfinding. Anobjectonapendulumwithalongstringis
furtherawayfrom the axisof the pendulum.Thismeansthatithas to covera longerdistance toreturn
to where itcame from.This isthe 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.

2. Sources of Error
Sourcesof Error:
- The time for one oscillationwasslightlyinaccurateasfrictiondue toair resistance slowsthe
pendulumdownwitheachswing.
- The time for twentyoscillationswasslightlyinaccuratedue tothe time taken(human
reactiontime) tostart and stopthe watch.
- There was uncertaintyinthe reference pointatwhichtostart and the stop the watch.
- There wasa bitof uncertaintyaboutwhichpointof swingtotime.
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.