Objective:
The experiment aims to calculate the constant π using the period of a pendulum.
Theory:
This is derived from the fact that the pendulums when thrown from a small enough angle displacement produce basic harmonic motion. From the formulas of basic harmonic motion, we know the period of a pendulum oscillating is:
T=2π√(L/g)
Where T is the period, L is the length of the pendulum and g is the gravitational constant on Earth.
Doing some manipulation on the equation, we get:
π=T/2 √(g/L)
of which we can use to calculate the constant in question.
Procedure:
Firstly a pendulum was creating by taping a thin rope to a pong ball. After that, the rope was taped high above to create a pendulum.
The experiment will use pendulums of different length which has been measured using a ruler. Then the pendulums will be thrown with a small angle displacement to produce oscillation. The time of a period will be calculated using a slow-mo camera operating at which will be evaluated using video to image sequence software. Basically, every frame of the video will become a seperate image. From there, the time it took between frames will be determined. Using the frames to count periods, we can be much more approximate than using the human eye and a chronometer to attain time. Every period is the time it took for the ball to do a back and forth swing.
For example, let the ball be released at frame 1000 and the ball comes to the release point at frame 1400. As such, the period will be 400 frames.
After calculating 9-10 periods, the average period will be calculated through arithmetic mean. Putting this into the equation we will get an approximate value for π.
