If the frequency of a simple harmonic oscillator is doubled, what happens to its period? (2021)

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Q: If the frequency of a simple harmonic oscillator is doubled, what happens to its period? (2021)

Solution: The period T is inversely proportional to frequency f. If f is doubled, T is halved.

Steps: 6

Step 1: Understand the terms 'frequency' and 'period'. Frequency (f) is how many times something happens in a second, while period (T) is the time it takes for one complete cycle.
Step 2: Know the relationship between frequency and period. The period T is inversely proportional to frequency f, which means if one goes up, the other goes down.
Step 3: If the frequency is doubled, it means f becomes 2f. Since T is inversely proportional to f, we can say T = 1/f.
Step 4: Substitute the new frequency into the equation. If f is now 2f, then T = 1/(2f).
Step 5: Compare the new period to the old period. The old period was T = 1/f. The new period is T = 1/(2f), which is half of the old period.
Step 6: Conclude that if the frequency is doubled, the period is halved.