Digitizing Pendulum Oscillations
================================

The nature of oscillations of a pendulum can be studied by digitizing the angular
displacement as a function of time. By fitting this data with a sinusoid, the
time period can be extracted. However, it is much cheaper to digitize the velocity
of the pendulum, using a simple DVD motor. Attaching the pendulm to the axis of the
motor and oscillating it induces voltage, proportional to the angular velocity
of the pendulum.

Objective
---------

Digitize the angular velocity of a rod pendulum and calculate the value of 'g'
from it.

Procedure
---------

.. image:: schematics/pend-digitize.svg
	   :width: 350px

-  Attach some sort of rigid pendulum to the axis of the motor.
-  Connect the motor between A3 and GND
-  Connect :math:`100~\Omega` resistor from Rg to Ground
-  Oscillate the pendulum and START digitizing

.. image:: pics/pendulum-screen.png
	   :width: 400px

Discussion
----------

The observed waveform is shown in figure. Fitting it with equation
:math:`A = A_0 \sin(\omega t + \theta) \exp( − Dt) + C`, using Grace gave an
angular frequency of :math:`10~Hz`.

The pendulum should be made with a heavy bob and a light weight rod
connecting it to the axis of the motor. In this case, the DC motor acts
like a generator and the voltage is proportional to the instantaneous
angular velocity.
