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Mathematics

Second-Order Differential Equations

Quick fact

The equation for a simple pendulum—one of the most famous second-order ODEs—was first derived by the Dutch scientist Christiaan Huygens in 1673, and it is still used to calibrate mechanical clocks today.

Why this is interesting

You push a child on a swing, and it moves not just once but with a rhythm that gradually fades. Why does it swing back and forth, and why does it eventually stop? The answer lives inside a second-order differential equation.