Question

find the fundamental period and fundamental frequency of the given function, g(t). () = 5 sin(10) 3 cos(12)

Answer 1

The fundamental period of g(t) is 60 and the fundamental frequency is 1/60.

Step-by-step explanation:

To find the fundamental period and fundamental frequency of the given function, we need to determine the values of the sinusoidal functions. In this case, g(t) = 5sin(10t) + 3cos(12t).

The fundamental period of a sinusoidal function is the smallest positive value of t for which the function repeats its pattern.

To find the fundamental period, we need to find the least common multiple (LCM) of the periods of the two functions, which are 2π/10 and 2π/12.

The LCM of 10 and 12 is 60, so the fundamental period of g(t) is 60.

The fundamental frequency of a sinusoidal function is the reciprocal of its fundamental period.

Therefore, the fundamental frequency of g(t) is 1/60.