Period of a sum of cosine signals

AI Thread Summary
The signal x(t) = 2 + 4cos(40Pi*t) + 3cos(60Pi*t) + 4cos(120Pi*t) consists of multiple cosine components with different frequencies. The fundamental frequency is identified as 10 Hz, leading to a calculated period of 0.1 seconds. However, the individual components have different periods: 0.05 seconds for the first cosine, 0.0333 seconds for the second, and 0.0167 seconds for the third. The overall period of the combined signal is determined by the least common multiple of these individual periods, which is 0.3 seconds. Understanding the period of each component is crucial for accurately determining the overall signal's behavior.
Quincy
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Homework Statement


Find the period of the signal x(t) = 2 + 4cos(40Pi*t) + 3cos(60Pi*t) + 4cos(120Pi*t).


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The Attempt at a Solution



The fundamental frequency (fo) = 10 Hz, since that's the greatest common factor of all the frequencies of the cosine signals. So the period would be 1/10 = 0.1 s. But my professor took points off for it, why?
 
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how many times per sec does each component of the signal by itself repeat?

How much time does each component of the signal take to go through one cycle?
 

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