Based on a video of the Bumble Ball played in slow motion, available at the link below, it appears that the bumble ball vibrates at a frequency of 8 vibrations per second (as counted with the video played at x0.25 speed). This measurement is most easily determined within the first few seconds of the video when it is being held, as once the ball is on the ground, the vibration of the ball itself is obscured by its contact with the ground (and subsequent contact with the dog).
Assuming that by amplitude, you mean the magnitude of displacement caused by each pulsing vibration, I will again draw my estimate from the video for the duration that the ball is held. This won't be very accurate because the hand holding the bumble ball in place is acting as a constraining force; however, as I have neither a laser system nor an accelerometer with which to precisely measure the amplitude of the physical vibration of a bumble ball- this will have to do.
I then took two screenshots of the video at different peaks of displacement of a single vibration (Fig 1. And Fig. 2). In each screenshot, I made a line measuring the distance between the two opposite spikes of the ball, a length known to measure 4.5 inches (though since the measurement was taken on a 2 dimensional representation of a 3-dimensional image, this is another weakness in our methodology of measurement).
I then placed the images on top of one another in Photoshop, setting the transparency of the top layer to 50% so that both shots were visible. I then made a separate file (Fig. 3) to directly compare the lengths of the ball in each image to see that the apparent length of the ball was the same in both images, thus confirming that our estimate will be at least somewhat accurate since our perception of the ball in each image is similar enough to render a useful measurement of the ball’s displacement from one image to the next.
At this point, I created an image which measured the length of the distance between the locations of a single point on the ball in the two images (Fig. 4). I used the corner of one spike on the ball, as it was easiest to see on this overlayed image. This length, the vector of displacement (s), was then measured using Photoshop’s image tools (Fig. 5).
I used the proportion between the length of the ball (4.5”) and the length of the line representing the length of the ball in Photoshop (5”) to determine the actual (approximate) displacement (s). By measuring the length of vector (s) in Photoshop (9.5/16 of an inch), and knowing the relation of this measurement to actual measurement (4.5:5), I found that the magnitude of displacement, or amplitude of the ball’s vibration, was equal to 8.1/16 of an inch, or approximately 0.5 inches per vibration.
I hope this information helps!
on January 22, 2015