Which one of the phrase is correct?

I did it in a short time period.
I did it in a short period of time.

TIME PERIOD or period of time?
Hi, I searched for both phrases on Google. Maybe ‘time period’ is frequently used to refer to geology and history. To me, ‘time period’ refers to something that has earned a place in a museum or in the history books. Contrast this with ‘period of time’ which is used to refer to current events and day-to-day occurrences. I did find something on the net about both phrases that reads like so: “The only kinds of periods meant by people who use this phrase are periods of time, so it’s a redundancy. Simply say “time” or “period."
Thanks. Very interesting.

Then I can say:

I did it in a short time.
I did it in a short period.
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A short period of time is better.

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I did it in a short period does not sound at all natural.

Time/period are not interchangeable in this way.

'I did it quickly' would be best but otherwise I did it in a short period of time.
short period of time
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I did it in a short time period (correct)