## PicoScope 5000 Series

#### FlexRes® Oscilloscopes

High speed and high resolution. Breakthrough ADC technology switches from 8 to 16 bits in the same oscilloscope.

# Measuring the swing of a pendulum

## An investigation into simple harmonic motion

This application note describes the use of the ADC-11 high-speed data logger to record the positional information of a swinging pendulum. Please note this experiment can also be done using the resistance input of the DrDAQ data logger.

## Contents

• Items used
• Experiment setup
• Experiment results
• Discussion of results

## Items used

• 100k linear potentiometer.
• 2.5 V voltage reference - Ref25 shunt reference used.
• High-speed data logger - the ADC-11 was used.
• Homemade pendulum system.

The circuit was constructed as shown below - the voltage range over the maximum swing was from 0 to about 1.2 V with 0.6 V being the centre rest position

## Setup

The experiment was set up as shown below with the potentiometer fitted to a piece of aluminum held in a bench vice. The pendulum was repeatedly released from the same height to find the time taken for the pendulum to stop - this was just less than 80 seconds.

PicoLog was therefore set up in 'Fast Block' mode to capture data at high speed over 80 seconds.

## Results

The PicoLog graph below clearly shows the results.

## Discussion of experiment results

The following formula for the oscillation of a pendulum can be derived from first principles:

where g = 9.78 m/s2 and l = 0.76 m

At a given place on the earth, where g is constant, the formula shows that the oscillation period T depends only on the length, l, of the pendulum. Moreover, the period remains constant even when the amplitude of the vibration diminishes due to the losses in the system such as the resistance of the air and friction of the potentiometer.

Since we do not have a point-sized mass we have to make an assumption about the effective length of the pendulum. The length, l, used here is the length of the rod (0.7 m) + length of suspending wire (0.015 m) + half the length of the mass (0.045 m), giving a total effective length of 0.76 m.

This gives a theoretical oscillation period of approximately 1.75 seconds.

Using the graph above we can count 35 oscillations over 60 seconds, giving an oscillation period of approximately 1.71 seconds. The result therefore agrees well with the calculations above allowing for the assumptions made.