Question

The periodic function $f(t)=A\sin \omega t$ repeats itself after

• A. $2\pi$
• B. $3\pi$
• C. $\pi$
• D. $\pi /2$

Answer 1

Answer: (A)

A periodic function repeats itself after a time period $T$.
Given, $f(t)=A\sin \omega t$
If the argument of this function $\omega t$, is increased by an integral multiple of $2\pi$ radians. Then, the value of the function remains the same. The given function $f(t)$ is then periodic and repeats itself after every $2\pi$ radians.
$\Rightarrow f(t)=f(t+T)$