My lecturer said that when a oscillating body loses energy in the form of radiation the natural frequency of oscillation is equal to the frequency of the emitted radiation. Can someone explain why?
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I don't see what this has to do with the title.
Anyway, if you oscillate one end of a long rope (the equivalent of the electromagnetic field in this case) with your hand (the equivalent of the oscillating body in this case) at frequency $\omega$ then the propagating wave in the rope will oscillate at the same frequency. This is an intuitive analogy to oscillating charged particles and electromagnetic waves.