Problem 75 - Algebra and Trigonometry

Question

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I analyzed simple harmonic motion in which the period was 10 seconds and the frequency was 0.2 oscillation per second.

Step-by-Step Solution

Answer

The statement does not make sense as it contradicts the fundamental understanding that the period is the reciprocal of the frequency in simple harmonic motion.

Step 1: Identify Key Parameters

In this statement, the period (T) is given as 10 seconds and the frequency (f) is given as 0.2 oscillations per second.

Step 2: Recall the Relationship between Period and Frequency

From learning about simple harmonic motion, the period (T) and frequency (f) are reciprocal to each other, following this formula: \( f = \frac{1}{T} \).

Step 3: Calculate Theoretical Frequency

Using the provided period in the relationship, the reciprocal of period 10 seconds yields a frequency of \( f = \frac{1}{T} = \frac{1}{10} = 0.1 \) oscillations per second.

Step 4: Compare Calculated Frequency with Given Frequency

The calculated frequency of 0.1 does not match the given frequency of 0.2 oscillations per second.

Step 5: Conclusion

Therefore, the statement does not make sense because the given period and frequency do not comply with the reciprocal relationship of frequency and period in simple harmonic motion.