What are the frequency and period for the given values and calculations?
Understand the Problem
The question pertains to calculations involving frequency and period in a physics context. It appears to include examples that demonstrate how to calculate frequency (f) and period (T) using given values.
Answer
The frequency and period relationship is given by $T = \frac{1}{f}$. For $f = 5 \text{ Hz}$, $T = 0.2 \text{ seconds}$; for $f = 12.1 \text{ Hz}$, $T \approx 0.08264 \text{ seconds}$.
Answer for screen readers
The relationship between frequency and period is accurately calculated using $T = \frac{1}{f}$.
Example calculations shown lead to:
For $f = 5 \text{ Hz}$, $T = 0.2 \text{ seconds}$.
For $f = 12.1 \text{ Hz}$, $T \approx 0.08264 \text{ seconds}$.
Steps to Solve

Understanding Frequency and Period Definitions
Frequency ($f$) is the number of cycles per second, measured in Hertz (Hz). The period ($T$) is the time for one complete cycle, measured in seconds. The relationship between them is given by the equation:
$$ T = \frac{1}{f} $$
and
$$ f = \frac{1}{T} $$ 
Calculating from Given Data
For example, if you have a frequency of 5 Hz, to find the period, use the formula:
$$ T = \frac{1}{5 \text{ Hz}} = 0.2 \text{ seconds} $$ 
Using Example Data
In the provided example, the calculations show a frequency of ( f = 5 \text{ Hz} ) leading to a period of ( T = 0.2 \text{ seconds} ). Verify with each given frequency to ensure the relationships hold true. 
Calculating for Different Frequencies
If given another frequency such as ( f = 12.1 \text{ Hz} ), calculate the period as follows:
$$ T = \frac{1}{12.1 \text{ Hz}} \approx 0.08264 \text{ seconds} $$ 
Summarizing Results
After verifying each frequency and period calculation, sum up all calculated periods and frequencies to have a clear understanding.
The relationship between frequency and period is accurately calculated using $T = \frac{1}{f}$.
Example calculations shown lead to:
For $f = 5 \text{ Hz}$, $T = 0.2 \text{ seconds}$.
For $f = 12.1 \text{ Hz}$, $T \approx 0.08264 \text{ seconds}$.
More Information
Frequency and period are key elements in wave mechanics, representing how often a wave cycle occurs and how long it takes, respectively. Understanding their relationship allows for better comprehension of various physical phenomena.
Tips
 Mixing up frequency and period: It's crucial to remember that frequency is the inverse of period. If you confuse them, your calculations will be incorrect.
 Forgetting units: Always include units in your calculations to avoid confusion, e.g., Hz for frequency and seconds for period.