### AN ACCURATE TIME MEASUREMENT TECHNIQUE IN PENDULUM EXPERIMENTS

#### Abstract

The acceleration due to gravity is normally determined in elementaryPhysics laboratories using the compound pendulum or Kater's pendulum U.The SUccess of this experiment largely depends on the accurate measurementof the period of the pendulum. The error involved in this measurement is dueto the inaccurate switching on and switching off ofthe stop dock at the beginningand at the end of counting of oscillations. It appears that the percentageerror due to this operation can be reduced by counting a large number ofoscillations during a lengthy time interval. However, this might not producedesired results as the chances of making a mistake is high when counting a largenumber of oscillations. The following is one of the methods that is normallyused for the accurate determination of the period.In the first part of the experiment, the period of the pendulum is approximatelydetermined measuring time taken for about 100 oscillations. Then, inthe second part of the experiment, the pendulum is allowed to. swing withoutmaking any counts, for about ten minutes so that it performs a whole numberof oscillations. If this time interval is t and and the approximate period obtainedin the first part of the experiment is T, then the total number of oscillationswhich took place in the interval t is the integral part of tfT. If this integralpart is N, then the accurate period is tiN. It will be shown here that theincrease. of the time interval, t, beyond a certain value can lead to the increaseof the error of the period. The way in which t should be selected to achieveaccurate results will be discussed in this paper.

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