When investigating the movement of material bodies that are fixed to springs, threads suspended in one point, etc. taking place in the accelerating reference systems, consideration is usually made only to the change in position of the balance of bodies and it is claimed that bodies take this changed position of balance at the very beginning of acceleration. Elastic or positional forces in general caused by the effect of springs, threads or other relations are unreasonably disregarded. This way a serious mistake is made, as the latter forces, by accelerating the bodies, do not stop them in their new position of balance but make them swing around this position of balance. The amplitude of such swings, depending on initial conditions, may be rather big.
Due to this reason some allegations concerning phenomena taking place in the accelerating systems and solutions of the majority of respective problems are wrong. This is shown in the article by examining specific places in physics textbooks and some widely prevalent problems.
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