# 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

- Attach some sort of rigid pendulum to the axis of the motor.
- Connect the motor between A3 and GND
- Connect 100Ω resistor from Rg to Ground
- Oscillate the pendulum and START digitizing

# Discussion

The observed waveform is shown in figure. Fitting it with equation A=A0sin(ω t+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.