CSEC Physics Lab - Effect of string length on the period of a pendulum
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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.
CSEC Physics Lab - Effect of string length on the period of a pendulum
- 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.