What are harmonics and why odd harmonics are dangerous

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Any system (or an object) set into vibration / oscillations has its own natural frequency. In addition to its natural frequency it has tendency to vibrate at higher and lower frequencies as well, of course to a lower extent. If the natural frequency is F say, it vibrates at frequencies 2F 3F etc. These are higher harmonic frequencies of oscillations present with relatively loer amplitudes. What is dangerous depends on given situation and criterian.
 
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