The only two relevant dates in the sources are 1931 for Bush's torque amplifier, and 1886 for Kelvin's harmonic analyser.
2.
With modern technology such a calculation is trivially easy, but Ingersoll and Zobel recommend the use of harmonic analysers, which are the mechanical counterpart of today's spectrum analysers.
3.
A number of similar systems followed, notably those of Leonardo Torres y Quevedo, a Spanish physicist who built several machines for solving real and complex roots of polynomials; and Michelson and Stratton, whose Harmonic Analyser performed Fourier analysis, but using an array of 80 springs rather than Kelvin integrators.
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