Question

Equipment used:

Thread, dense spherical mass like a marble or a bearing, perhaps about 0.5 – 1.0 cm in diameter. Otherwise, use a
mass that is approximately spherical, e.g., a tangerine or apple.

Method of obtaining g:

Measure the period of 4 lengths of thread from 75 cm to 1.50 cm. Be sure to measure the length from the support
point to the center of mass of the spherical mass at the bottom end of the thread. For each length of thread, pull
the string from the bottom mass out to about 10 degrees from the vertical, then let the pendulum oscillate back
and forth 20 times while measuring the time with a stopwatch. Determine the period, T, by dividing the elapsed
time by 20.

Plot the period squared versus the length of the pendulum. The resulting curve should be a straight line with a
period involving the acceleration of gravity. Put your data for the length of the pendulum and the period squared
into Excel. Use LINEST to find the best fit slope for the data and the error in the slope. Calculate the acceleration of
gravity and the estimated error of the measurement for g.

Please give an excel file here.

Answer 1

We have plotted the pendulum period T2 (s2) vs String length L and its linear best-fit trendline. The y values represent the period T and x values represent the string length L.

The trendline equation:

The slope of the trendline:

The y-intercept of the trendline:

Therefore, the trendline equation:

We know that the period of the pendulum is expressed in terms of period P, string length L, and gravitational acceleration g:

From equation (1) and (2), the slope of the trendline is:

Therefore, the experimental value of gravitational acceleration is 8.3464 m/s2

The percentage difference between theoretical value and experimental value is given by: