What it shows
The square of a pendulum’s period is proportional to its length, with slope 4π² / g. The slope of the graph gives the acceleration due to gravity at your place.
The science
For small swings, a pendulum of length L has period T = 2π √(L / g), independent of the bob’s mass and the amplitude. Squaring gives T² = (4π² / g) L, a straight line through the origin of slope 4π² / g. The length L is measured from the point of suspension to the centre of the bob, that is thread length plus the bob’s radius. Timing many swings lowers the error in T. At Indian latitudes g is about 9.78 to 9.79 m/s².
Materials
Cost: free. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.
- A small metal ball or a nut as the bob
- Strong thin thread about 1.2 m long
- A stand or a split cork clamp fixed to a door frame or a shelf
- A metre rule and a vernier calliper or a ruler to measure the bob’s diameter
- A phone stopwatch
- A protractor to check small angles
- Graph paper
Safety
For this project: Release the bob gently and keep fingers away from the stand. An adult should supervise a tall setup.
Never use mains electricity: power models with cells, batteries or a low-voltage adapter. Sharp and hot tools, flames and lab chemicals need an adult or your teacher beside you. Keep magnets, button cells and small parts away from young children, and wash your hands after making.
All the safety rulesStep by step
7 steps. Do them in order, and test each part before you go on to the next. Write what you notice in a notebook as you go.
Fix the thread between two halves of a split cork clamped to the stand, so that the pendulum swings from a fixed point.
Set the length from the clamp to the bob centre to 100 cm; measure the thread length and add the bob radius.
Displace the bob by about 5 cm (less than 10 degrees) and release it, then time 20 complete oscillations; count the first swing as zero as it passes the centre.
Calculate T by dividing the time by 20 and repeat for the same length twice more to average.
Repeat for lengths 80, 60, 50, 40 and 30 cm.
Calculate T² for every row and plot T² (y axis) against L (x axis); draw the best straight line.
Find the slope and calculate g = 4π² / slope; compare with 9.8 m/s² and find the percentage error.
What you should see
The T² against L graph is a straight line through the origin, and the value of g found from its slope is within 2 to 5 percent of 9.8 m/s².
Viva questions
A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.
1What does the period of a simple pendulum depend on?
Only on its length and on g, not on the mass or on a small amplitude.
2Why is L measured to the centre of the bob?
The effective length of the pendulum is measured to the bob’s centre of mass.
3Why count 20 oscillations?
It lowers the effect of reaction time in starting and stopping the watch.
4What would the period be on the Moon?
Longer, about 2.4 times, since g on the Moon is about one sixth of Earth’s.
Take it further
Measure T for angles of 5, 20, 40 and 60 degrees and see how the period starts to rise at large amplitudes.
Change one thing, measure what happens, and add a table or chart of your readings: that is what turns a model into your own investigation.
Free ebooks for this project
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