.. 6.2

Angular Velocity of Pendulum
============================

**Objective**

To study the nature of oscillations of a pendulum. An angle encoder is
required for measuring the angular displacement as a function of time.
But using a DC motor as a sensor, we can measure the angular velocity as
a function of time.\begin_inset Separator latexpar\end_inset

.. image:: pics/pendulum-screen.png
	   :width: 300px

**Procedure**

-  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

**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.
