Cyclotron Observation

I don't have any cyclotron, i was just revising my topics for JEE in 2023, and while studying the topic, got to know and understood why "the voltage applied across cyclotron terminals should have same frequecy as that of revolution of the charge particle so that when it reaches from one D to another D, the polarity of that D changes such that it allows the particle to enter from that side and complete another half cycle.

while i was reading this i though what if the voltage frequency is not same as that of the particles motion? won't it be working normally? then i started putting multiples of circular motion frequency of particle as applied voltage frequency and observed that if the voltage frequency is odd multiple of that of particle motion, the particle still enters the another D with same polarity as that was in case of same frequencies.

Then I put the graph of the observation too, and the critical positions of the particle where certain polarity was required to comlete the cycle was still being the same on the graph when i was drawing graphs for odd multiples of voltage frequencies. I culd nto add video here, but I had uploaded one long ago that day. The link is at the bottom of this page. There is smething more in that post too, regarding the observation of AI on the same topic.

See this muight be nothing of great interest to you, but when i wanted to know this, the curiosity of mine was not solved by any post online, I found the solution myself, and later for veification, I tried AIs but most of them were wrong. Hence discovering something myself while just studying on pages, was something more than normal for me, no matter if it is of any work or not, I got more interest in thinking about things that day.

Blogger post : https://nirbhikviswasofficial.blogspot.com/2023/04/can-cyclotron-voltage-frequency-be-any.html