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In school we have numerous exercises that ask you to find the time when a body passes a certain point for the nth time in simple harmonic oscillation. But it is a bit mentally taxing to solve with the actual formula of x=Asin(ωt + φ), just because you have to sort out all the infinite solutions. It is even worse when you get to more challenging tasks like for example having to find various time intervals when the body gets from point A to point B. So I was wondering if it is possible to have a function f(t)=S where S is the distance travelled . This function must be 1-1 ( S is always increasing) and thus give only one solution. Then it must be relatively easy to get S from x and the opposite for any other possible calculations.