Place the Sonic Ranger roughly 1 m from
the stationary pendulum bob,
then start the pendulum moving away
and towards the Sonic Ranger.
Using the Ranger software,
measure the bob's horizontal displacement x(t). For small
amplitude motion, the displacement
,
so that the displacement is given by
Once you have a good measurement of x(t)
without any loss of signal etc., calculate
the corresponding
and
.
Draw a graph of
,
using a common time axis. Briefly discuss the relative
phases of the three graphs.
Calculate the period and angular frequency of the pendulum's motion.
Recall that
.
Think about how to make
the most accurate measurement of these quantities from your data,
and describe your procedure.
Measure the frequency of the pendulum motion
for several different amplitudes of
the oscillation.
Measure the length l of the pendulum, from the pivot point to the center of the bob. Using the relationship
calculate the acceleration due to gravity g. Repeat this for a different value of the string length l. Compare your results for g with that obtained in the airtrack measurement and discuss which technique you expect to be more precise.