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Most of the world's currently-operational nuclear reactors were built in the 1970s and 80s and with an expected lifespan of 30–40 years are coming to the end of their predicted lifetime. Many will need to be decommissioned in the not-too-distant future.
Bertrand's Paradox is an illustration of the need to define the mechanism for picking a random variable carefully for its associated probability to be well-defined.
The previous blog post described the normal modes of a chain swinging under its own weight. Here we describe the motion of a chain after an arbitrary displacement as a linear combination of such normal modes.
The description of the oscillations of a hanging chain was a problem in mechanics solved by Daniel Bernoulli in the 18th century and which led to the discovery of the class of functions known as Bessel functions.