Question

For a periodic signal $v(t) = 30\sin(100t) + 10\cos(300t) + 6\sin(500t + \pi/4)$, the fundamental frequency in rad/s is

• A. 100
• B. 300
• C. 500
• D. 1500

Hint:

For periodic signals, the fundamental frequency is the GCD of all individual angular frequencies.

Answer 1

The Correct Option is A

Step 1: Identify angular frequencies.
From the given signal:
\[ \omega_1 = 100,\quad \omega_2 = 300,\quad \omega_3 = 500 \text{ rad/s} \]
Step 2: Determine fundamental angular frequency.
The fundamental frequency is the greatest common divisor (GCD) of all angular frequencies.
Step 3: Compute GCD.
\[ \gcd(100, 300, 500) = 100 \]
Step 4: Final conclusion.
Hence, the fundamental angular frequency of the signal is 100 rad/s.