MadSci Network: Physics |
Think about a pendulum, with a solid rod connecting the bob instead of a string. Shorter the pendulum is, the faster it swings to and fro. That is, it has a lower time period of oscillation or a higher natural frequency. Now, think of inverted pendulums (pivoted at the bottom). Their time periods are going to show the same behaviour (longer, slower), but this time it is unstable, as opposed to an upright one which always tends to seek its equilibrium position. Your markers are like inverted pendulums, with the fingertip as the pivot.A slower one will give you more time for the reflexes you have, and that's why its easier to balance a longer one. There are deeper issues here, which are advanced for you. However, you should remember this question, because it is an excellent way to learn about control systems and stability theory, which someday you might need (much later).
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