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I am trying to generate a graph of a sinusoidally oscillation against time. However, the time itself is passing sinusodally, i.e time flows faster at some points and slower at others. I'm doing this as I need test data for a program I've written to decode real world data I'm generating which comes in this format.

Here is an excel graph of the closest I've come (amplitude = sin(time*sin(time))), however this is not quite correct, as it goes off as time increases (as the time between oscillations get closer and closer. but between t=10 and t =20 you can get a good idea of what I'm after.)

I have also stuck a very crude sketch of the type of output I desire. What's the mathematical form of this?

Many thanks for your help.

C x