Laplace Transform of $f(t) = u(\sin(2t))$?

Question

What is the Laplace Transform of $f(t) = u(\sin(2t))$?

I'm confused how to proceed further? because $u(t)=0$ for t<0. What does having $\sin(2t)$ in argument mean?

Or $u$ has to be taken as unknown function?

Answer 1

If $u(t) = 1$ for positive $t$, and $0$ otherwise, then $u(\sin(2t)) = 1$ whenever $\sin(2t)$ is positive.

That is, $f(t) = 1$ whenever $2t$ is in one of the intervals $(0,\pi),\;(2\pi,3\pi),\;(4\pi,5\pi),\;(-2\pi,-\pi),\;\cdots$

meaning $t$ is in one of the intervals $(0,\frac\pi2),\;(\pi,\frac{3\pi}2),\;(2\pi,\frac{5\pi}2),\;(-\pi,-\frac\pi2),\;\cdots$

and $f(t) = 0$ otherwise. This is a square wave.