Problem 75 - Precalculus Essentials

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 because the period and frequency given do not follow the reciprocal relationship, as the frequency should be 0.1 Hz, not 0.2 Hz if the period is 10 seconds.

Step 1: Understanding the Definitions

Firstly, define the terms. The period (T) is the time taken for one complete oscillation. It is measured in seconds. The frequency (f) refers to the number of oscillations that occur in one second. It is measured in Hertz (Hz) or oscillations per second. There is a reciprocal relationship between them: f = 1/T and T = 1/f. This means if you know one, you can calculate the other.

Step 2: Check the Given Statements

According to the statement, the period T is 10 seconds and frequency f is 0.2 Hz. Therefore, check if the given values are consistent with the reciprocal relationship. If the reciprocal of the period T (1/T) equals the frequency f given in the statement, then the statement makes sense. Calculate 1/T, which equals 1/10 = 0.1 Hz.

Step 3: Compare the Results

Finally, compare the calculated frequency with the given frequency in the statement. The calculated frequency (0.1 Hz) is not equal to the given frequency (0.2 Hz), which indicates that the statement does not make sense.