Datalogging in Science

Oscillations of a spring SHM

Simple harmonic motion

Overview
In this demonstration, the Motion Sensor is used to monitor the position of a mass oscillating on the end of a spring. Any motion that repeats itself is described as harmonic motion. The software processes the data to produce graphs of displacement, velocity and acceleration, in each case as a function of time. It will be possible to show that the motion of the spring is simple harmonic motion (SHM).

Theory
The acceleration (and hence the restoring force) is always directed towards the centre of oscillation. The magnitude of the acceleration is proportional to the displacement from the mean position.

Apparatus

Datalogger capable of fast logging

Motion Sensor with the range set to distance (metres),

Steel spring and hanging mass (the spring-mass system needs to have a period of at least one second).

Retort stand with bosses and clamps,

Large G clamp.

Procedure
1. Assemble the apparatus as shown. Make sure that the apparatus is as rigid as possible. (See Precautions below)
All clamps must be firmly tightened.

2. Connect the Motion sensor to the datalogger.


3. Connect the datalogger to the computer.


4. Launch the Graph program and set it to record distance in Fast mode.

5. Set the mass oscillating, by pulling it down and releasing it.

6. Begin datalogging.

7. The software will retrieve and display the results, which will be a Distance versus Time curve.


8. Check that the trace is even. If so, save the recording on the computer. if not erase the data and re-run the experiment.


9. Optimize the view of the graph on the computer screen.


10. Use the Function Wizard to produce graphs of velocity against time and acceleration against.

Precaution:
A guard should be used to protect the Motion sensor from accidental damage.


The mesh on the guard must be large enough to let the ultrasound from the Motion Sensor through.


The oscillations must not overstretch the spring.

Check that the ultrasound cone of the Motion Sensor does not reflect off any part of the bench.


A 'target' for the Motion Sensor will have to be added to the bottom of the mass
carrier. A square of paper or stiff card 6 x 6cm works well.


Check that the oscillating mass does not get closer than 17cm to the Motion Sensor, or more than 50cm away from it, and that it is oscillating vertically.

Results

Sample results are shown below (after zooming in to examine in detail).
Use the analysis features of the software to examine the motion graphs you obtain and draw conclusions about the characteristics of simple harmonic motion

The velocity against time graph has been added using the Function Wizard

Questions
Where is the body when;
1 its acceleration is zero?
2. its acceleration is a maximum?
3. its velocity is zero?
4. its velocity is a maximum?

How would you define simple harmonic motion?

What everyday examples of simple harmonic motion can you think of?

Data Harvest users

1. Connect the sensor to the datalogger and the logger to the computer
2. Then click the Set Up icon to the right of this message.
3. When the software opens, click the Play button.