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How to find out experimentally to measure the vibrational frequency of some type of spring without electronic or electrical instrument?

I am just wondering about the advance stage of the discovery of the theory of vibrations it became in the 19th century

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A fairly straightforward way to do this is to have the sample spring connected via a mechanical linkage to a device which traces a line on a moving spool or drum using ink on paper or similar.

These sorts of paper trace devices were used until relatively recently for all kinds of devices to measure some variable over time, barometers like this are very common.

As long as you know the speed that the paper spool is moving in the y axis and the relationship between the extension of the spring and the x axis you can get pretty accurate displacement vs time recordings.

Obviously the technology to do this is very similar to that of clocks and watches.

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  • $\begingroup$ but how come the spool or drum is moving at constant speed? $\endgroup$
    – Victor
    Jan 16 '16 at 18:51
  • $\begingroup$ Basically the same way that a clock does. There are lots of mechanical ways to achieve a constant speed drive as that's the fundamental requirement of a mechanical clock. In clockwork one of simplest ways to do this is with a pendulum escapement mechanism but depending on the exact requirements of the experiment there are other ways to do it including regulators which act as analogues of electronic control systems. $\endgroup$ Jan 16 '16 at 19:18
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If the frequency is high enough, its sound can be compared to a tuning fork, ref https://en.wikipedia.org/wiki/Tuning_fork

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