An oscillating cart with a PocketLab provides an interesting way to study Newton's Second Law of Motion as well as some principles of damped harmonic motion. The apparatus setup is shown in the figure below. The small dynamics cart that can quickly be made from parts included in the PocketLab Maker Kit is shown in its equilibrium position. Rubber bands are attached to each side of the cart and to two ring stands weighted down with some heavy books. It is best to use rubber bands that provide as small Newton/meter as possible. PocketLab is attached to the cart with its x-axis parallel to the rubber bands.
The close-up in the figure below shows that two small pieces of wire are threaded into holes in the cart with the rubber bands attached. The ends of each wire are twisted together to tighten the rubber band on the cart.
The movie below shows a typical run, with 20 data points per second and acceleration selected in single-graph mode. The red trace on the graph is the acceleration of interest, namely acceleration in the X-direction. The blue and green traces, representing acceleration in the Y and Z directions, are quite erratic due to slight jiggling of the cart, and are not of interest here. The red curve shows a very regular pattern, in which it can be observed that the magnitude of the acceleration is greatest when the cart is at each end of its swing and zero in the center of the swing. It is also noted that the magnitude of the acceleration decreases with time in a pattern that suggests exponential decay.
The image shown below contains a graph of x acceleration from data produced by the PocketLab app. The graph was obtained by importing data from the PocketLab app into Logger Pro, an exceptional educational scientific analysis software from Vernier Software & Technology (vernier.com). A model involving the sine function and exponential function was created. It is seen that the model (the black curve) follows the red acceleration X curve very well.
This experiment allows one to do a quantitative investigation of the damped harmonic motion of a swinging pendulum. The pendulum is a piece of wood about a yard long from a Michael's hobby shop one end of which has been attached to a PocketLab by a rubber band. The other end is taped to the top of a doorway, allowing the resultant pendulum to swing back-and-forth as shown in the image below.
The y-axis is perpendicular to the XZ plane of the swinging pendulum. Therefore, the main item of interest is the magnitude of the angular velocity vector in the Y direction (shown as a blue curve in the movie).
The image shown below contains a graph of the Y angular velocity (shown in blue). The X and Z angular velocities (shown in red and green in the video, respectively) are small and erratic due to slight wobble in the swinging pendulum and are not included in the graph. The graph was obtained by importing the data from the PocketLab app into Logger Pro, an exceptional educational scientific analysis software from Vernier Software & Technology (vernier.com). A model involving the sine function and the exponential function was created. It is seen that the model (the black curve) follows the blue angular velocity curve very well.