12 juni 2024
Probabalistic Analysis of Classical Oscillator
This virtual lab serves as a bridge from classical mechanics to the inherently probabilistic nature of quantum theory. It allows students to analyze a classical system, here a block oscillating on a spring, in a probabilistic way. This is achieved through a photographer that takes snapshots (photos) of the oscillating block at random times. The position of the block is binned, building up a histogram of snapshot numbers versus position bins. Students can change the bin size, and convert the snapshot histogram into a probability density histogram. They can also display the theoretical probability density histogram, as well as the theoretical probability density curve as the bin size tends to zero. Students can see that the more measurements they take, the smaller on average the deviations of their data from the theoretical values. A second tab allows students to solve a number of challenges. The challenges probe the primary aims outlined below. Primary aims: Students can describe the experimental procedure shown in the lab for analyzing a classical system in a probabilistic way. Students can describe qualitatively how the block’s speed in a given region relates to the number of snapshots in that region. Students understand the difference between a probability and a probability density. They can perform calculations to find probabilities and probability densities from the number of snapshots in a given region.