The smallest period of f(x)=(nx/k) is (take n,k positive)

GATE 2019 MT – Question 13

Engineering Mathematics · Calculus and vector calculus · 1 mark · Multiple choice

The smallest period of $f(x)=\sin(nx/k)$ is (take n,k positive)

$2\pi$
$k/n$
$2\pi k/n$
$2\pi n/k$

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Show answer and explanation

Correct answer: (C) $2\pi k/n$

Explanation

The sine argument must advance by 2π for one full cycle. Therefore nT/k=2π and T=2πk/n, C. If signed parameters were allowed the positive period would use |k/n|.

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