Question

2) Another student measured the period of a simple pendulum using a stopwatch. However, instead of measuring a single period, he waited for 10 periods to elapse before stopping the stopwatch. He obtained the time t = 19.40 s for ten oscillations. Report the period and its uncertainty in an appropriate format (assuming that the absolute uncertainty in the time measurement is still the same, i.e. 8t = 0.2 s). Calculate the fractional uncertainty in the period measurement.

Answer 1

Time of 10 periods =19.40s

Time of 1 period(Time-period)=19.40/10=1.94s

And uncertainty is given as Δt=0.2s.

So the time period(T)=(1.94±0.2)s.

Fractional uncertainty =Δt/T=0.2/1.94=0.103.