The GATE Grind

GATE 2021 IN – Question 18

Signals and Systems · Signals and linear time-invariant systems · 1 mark · Multiple choice

The signal $\sin(\sqrt{2\pi t})$ is ______.

  1. Periodic with $T=\sqrt{2\pi}$
  2. Not periodic
  3. Periodic with $T=2\pi$
  4. Periodic with $T=4\pi^2$

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Show answer and explanation

Correct answer: (B) Not periodic

Explanation

The phase is proportional to √t, not t. Its derivative decreases with time, so consecutive zero crossings have unequal spacing. No fixed positive T repeats the waveform for every t in its domain. The signal is **not periodic, B**.