What is the decade of experimentation that start to verify the formulas from mechanics of vibration?

Question

What is the decade of experimentation that start to verify the formulas from classical mechanics of vibration?

People unable to "see" or "hear" the vibration of the objects in the late 19 century...

Answer 1

In the early development of the theory of oscillations (vibrations), music played an important role. In fact, according to the legend, mathematical theory of vibrations begins with Pythagoras, and it was closely related to music theory. In 17s century Marine Mersenne discovered the precise law of vibration of a sting. He was a music theorist. Music (that you can hear) was the experimental verification of this mathematics.

In the later development Galileo and Huygens are important, they were interested in improving clocks. Good clocks were needed for determination of longitude at sea. Experimental verification of these theories were better cocks based on them.

With the invention of calculus, the theory of oscillations became a major area of mathematics with the range of applications to the real life so wide that I cannot even list the areas: almost all physical theories use it in some form. Electricity and magnetism, acoustics, all sorts of waves, quantum theory, etc. because of this extremely large number of applications, the theory is verified literally by everyone every day. Almost all devices around us use it in some form.