Wired breaks down the difficulties of modeling a pendulum’s swing.
A basic pendulum IS a mass at the end of a string that swings back and forth. It seems simple, and it appears in most introductory physics textbooks. But it’s not a trivial problem to solve for the motion of this mass on a string.
Traditionally, the introductory view of the pendulum is to show that for small amplitudes the motion of the mass is like a simple harmonic motion (motion of a mass on a spring) with a period of oscillation that depends on the length of the string and the local gravitational field.
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