Question

The period of the signal x(t)=10 sin 12 pi t + 4 cos 18 pi t is

Answer 1

Given: The signal x(t) = 10 sin 12πt + 4 cos 18πt

To find: The period of the given signal.

Solution:

• Now we have given the signal as function x(t) = 10 sin 12πt + 4 cos 18πt.

• So now, sin 12πt has period of:

            = 2π/12π

            = 1/6

• cos 18πt has period of:

            = 2π/18π

            = 1/9

• Now the common period will be the LCM.

• So the lowest common factor is 1/3.

Answer:

      The period of the given signal x(t) = 10 sin 12πt + 4 cos 18πt is 1/3.

Answer 2

Answer:

Step-by-step explanation: As ratio of frequencies of both signal is rational.
The period of resultant signal will be either L.C.M. of their time periods or H.C.F. of their frequencies.
Hence H.C.F of 12π and 18π will be fundamental frequency of resultant signal i.e. 6π.

And by using relationship T=2π/w, we can calculate Time period

T = 2π/6π
i.e. T = 1/3 unit