Question

Galileo determined the relationship between the length of a pendulum and its period. Describe how you would design and execute an experiment to determine the relationship of a pendulum’s length and its period. How would you depict the results to make your analysis of the relationship clear?

Answer 1

A pendulum can be created using a small metal sphere with a small radius and a large mass as compared to the length and mass of the light string from which hangs. Once the pendulum is set into motion and swinging back and forth, the motion itself will be periodic. Here, T is the time period of pendulum taken to complete one oscillation. One oscillation contains back and forth single motion.

Here, we know that

1) The period of a simple pendulum of constant length is independent of its mass, size, shape or material.

2) The period of a simple pendulum is independent of the amplitude of oscillation, provided it is small.

Now, release the pendulum from some height and let it oscillate under gravity. Start the stopwatch at the instant of leaving the pendulum. Use an angle of less than 5 degrees. Count for 30 oscillations:Remember to divide by 30 to get the time for ONE oscillation.

Now, after dividing the time by 30, square the answer.

Now, draw a graph between T² and L.

It will be a straight line.

we will know that

T = 2$\pi$ (L/g)

so,

squaring both sides, we have

T² = 4$\pi$² * L/g

so, we can see that

T² is directly related to L.