Question

What is the fundamental period of the function s(t) = cos(2 pi 15 t) + cos(2pi 95 t) in seconds (if t is measures in seconds) ?

Answer 1

To find the fundamental period of s(t) = cos(2π×15t) + cos(2π×95t), calculate the periods of individual cosine functions and then find the LCM of these periods, which is 285 seconds.

Step-by-step explanation:

The student is asking for the fundamental period of the function s(t) = cos(2π×15t) + cos(2π×95t), where t represents time in seconds. To find the fundamental period of this function, we need to determine the periods of each individual cosine component and then find the least common multiple (LCM) of these two periods.

The period of a cosine function of the form cos(ωt) is T = ×240;/ω. Therefore, the periods of the individual cosine terms in s(t) are T1 = 1/15 s and T2 = 1/95 s, respectively. To obtain the fundamental period of s(t), we calculate the LCM of T1 and T2.

Since finding the LCM of two fractions is equivalent to finding the LCM of their denominators, we need to determine the LCM of 15 and 95. The LCM of 15 and 95 is 285. Therefore, the fundamental period of s(t) is T = 285 s.