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The origin of the Entscheidungsproblem goes back to Gottfried Leibniz, who in the seventeenth century, after having constructed a successful mechanical calculating machine, dreamt of building a machine that could manipulate symbols in order to determine the truth values of mathematical statements. [3]
A simple gravity pendulum [1] is an idealized mathematical model of a real pendulum. [2] [3] [4] It is a weight (or bob) on the end of a massless cord suspended from a pivot, without friction. Since in the model there is no frictional energy loss, when given an initial displacement it swings back and forth with a constant amplitude. The model ...
A decision problem is a yes-or-no question on an infinite set of inputs. It is traditional to define the decision problem as the set of possible inputs together with the set of inputs for which the answer is yes. [1] These inputs can be natural numbers, but can also be values of some other kind, like binary strings or strings over some other ...
Rayleigh–Lorentz pendulum (or Lorentz pendulum) is a simple pendulum, but subjected to a slowly varying frequency due to an external action (frequency is varied by varying the pendulum length), named after Lord Rayleigh and Hendrik Lorentz. [1] This problem formed the basis for the concept of adiabatic invariants in mechanics. On account of ...
Johann Bernoulli solved the problem in a paper (Acta Eruditorum, 1697). Schematic of a cycloidal pendulum. The tautochrone problem was studied by Huygens more closely when it was realized that a pendulum, which follows a circular path, was not isochronous and thus his pendulum clock would keep different time depending on how far the pendulum ...
Since the system is invariant under time reversal and translation, it is equivalent to say that the pendulum starts at the origin and is fired outwards: [1] r ( 0 ) = 0 {\displaystyle r(0)=0} The region close to the pivot is singular, since r {\displaystyle r} is close to zero and the equations of motion require dividing by r {\displaystyle r} .
Every helpful hint and clue for Thursday's Strands game from the New York Times.
"Simple gravity pendulum" model assumes no friction or air resistance. A pendulum is a device made of a weight suspended from a pivot so that it can swing freely. [1] When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position.