Human foot pendulum | SHM

Physics principles are best appreciated when they are applied to real life phenomena. This experiment gives a practice of equations of time period of a simple pendulum and of a physical pendulum in a very interesting novel situation.

Procedure

You need approx 2.5 ft high table, a stop watch (mobile stop watch will do) and measuring tape for this experiment.

1. Ask the person to sit on a table with both the legs hanging in air.
2. The person lets one of his/her legs oscillate about the knee joint. It will take some practice to let the leg go in most relaxed manner as if no effort is made to forcefully move it.
3. Measure the time of say 10 oscillations using your mobile stop watch. Get the time period. Fill in the table. You may like to repeat 3-4 times to get an average \(T_0\). Why repeating it 3-4 times is desirable at this step?
4. Measure the length of the leg from the knee to the bottom of the foot. Fill in the table.
5. Assuming that the oscillating leg can be approximated by a simple pendulum of same length, calculate the time period \(T_1=2\pi\sqrt{l/g}\).
6. Calculate the percentage error \(\frac{T_1-T_0}{T_1}\times 100\).
7. Now approximate the oscillating leg by a uniform rod of same length. Calculate the time period \(T_2=2\pi\sqrt{m}\). Here \(I\) is the moment of inertia of the leg about the axis of rotation, \(m\) is the mass of the leg and \(d\) is the distance of the center of the mass from the knee. Do you need the mass of the leg to calculate \(T_2\)?
8. Calculate the percentage error \(\frac{T_1-T_0}{T_1}\times 100\).
9. What is the percentage error expected in measuring the time period?

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