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  4. The periodic function f(t)=A sin ω t repeats itself after

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

Oscillations

Solution:

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.
$\Rightarrow f(t)=f(t+T)$