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If the experiments confirm the hypotheses, these are true and
the laws (formulas) deduced are valid. Then anyone can test them and
they always apply, everywhere, under the stated conditions.
A large number of confirmed hypotheses expressed in mathematical laws constitute part of a General Theory which explains all of them: The Law of the pendulum is part of Newton's Universal Law of Gravitation.
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Galileo assumed that the pendulum took the same time to
make one oscillation whether it was separated more or less from the
vertical and that this time did not depend on the mass.
Galileo had found out that a mass of 1 kg and another of
10 kg took the same time to fall from the top of the Tower of Pisa even
though they were thrown from different heights on the tower. And after
all the mass of the pendulum also fell guided by the rope.
This must have influenced the formulation of the initial hypothesis and
encouraged him to undertake the experiments. His intelligence, good
training and interest in making discoveries did the rest. The experiments demostrated the hypothesis.
If first hypotheses are not fulfilled, new ones must be made and all
the experiments must be re-thought to see if the new hypotheses are
confirmed.
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The General THeory which explains these facts was developed by Newton years later.
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