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A "double" pendulum consists of two simple pendulums with mass (m) and string of length (l). The string of the first pendulum is attached to the ceiling while the string of the second one is attached to the mass of the first pendulum, as shown. (A detailed analysis of this problem has been assigned to the PHY 311 Classical Dynamics students, but they've been warned against giving any hints!) Here's the puzzle.
Given the right initial start, can this double pendulum swing as one unit? That is, is it possible for the strings to stay aligned as they swing? Recall the formula for a "single" simple pendulum is |
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