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

schematics/pend-digitize.svg pics/pendulum-screen.png

Discussion

The observed waveform is shown in figure. Fitting it with equation A = A0sin(ωt + θ)exp(Dt) + C, using Grace gave an angular frequency of 10Hz.

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.