Strategy and Set-up
In order to calculate energy, the velocity must be known. To calculate velocity, our strategy is to measure position with respect to time, and then obtain the derivative to obtain the velocity using the forward, backward and central difference formulae.
To measure position versus time, a video with a fixed frame of the coupled pendulum in motion is taken. A stable tripod is used to facilitate this. A sample frame of the set-up we used is shown below. A top-view is chosen since the displacement perpendicular to the floor is small compared to the displacement parallel to the floor. Also, a ruler is placed in the center to allow measurement of the scaling from pixel to real distance by using ratio and proportion.
Sample frame of the coupled pendulum system viewed from above.
To make the measurement of position more efficient, image-processing techniques are used. The two golf balls have been colored with red and blue markers to facilitate image segmentation by thresholding and color histograms. Also, the segmented images were further cleaned using morphological operations. Below is an example of the segmented/isolate blue and red crosses. This shows how useful and practical the previous activities are in image processing.
After segmenting/isolating and cleaning the red and blue crosses, the respective positions of the centroids are obtained, hence measuring the position of the balls with respect to the fixed video frame.
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