Question

Given the periodic y-data below (assume that there are 6 samples taken each second), determine the amplitude of the lowest frequency cosine function in the periodic data fit: Y=[ 0.4000 0.2732 0.0000 -0.2000 -0.2000 -0.0732 0 -0.0732 -0.2000 -0.2000 -0.0000 0.2732 0.4000 0.2732

-0.0000 -0.2000 -0.2000 -0.0732 0 -0.0732 -0.2000 -0.2000 -0.0000 0.2732 0.4000];
Hint: You should plot the data to determine a single period of the data before applying the periodic data fit.

Answer 1

To find the amplitude of the lowest frequency cosine function in the periodic data, one must identify a single period and look for the maximum absolute y-value within that period. Here, the maximum value is 0.4000, which represents the amplitude of the cosine wave.

• To determine the amplitude of the lowest frequency cosine function in the given periodic data, we first need to identify a single period of the data.
• By examining the provided y-data, we notice that the data repeats itself, which signifies one period.
• A single period of the given data can be considered as [0.4000, 0.2732, 0.0000, -0.2000, -0.2000, -0.0732, 0, -0.0732, -0.2000, -0.2000, 0.0000, 0.2732, 0.4000].
• The amplitude of a cosine wave is the maximum absolute value of its displacement.
• In this set of data, the highest y-value is 0.4000, and since a cosine wave oscillates symmetrically above and below the horizontal axis, this value represents the amplitude of the wave.