Current vs. Time: Mathematical Expression for Hippolyte Pixii's Dynamo

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The discussion focuses on deriving the mathematical expression for the current generated by Hippolyte Pixii's dynamo, modeled as a cosine function. The maximum current is given as (2/pi)0.5 amperes, and the angular frequency is denoted as ω0. The time-domain signal for the alternating current can be expressed as I(t) = (2/pi)0.5 * cos(ω0 * t), where I(t) represents current at time t. The assumption is made that the magnet is already in motion with its pole positioned below the coil at time zero. This provides a clear framework for understanding the relationship between current and time in the context of this AC generator.
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Consider a simple alternating current generator such as Hippolyte Pixii's dynamo. The current generated by such dynamo can be described as simple oscillating cosine signal. Assuming for simplicity that the max current generated each time a pole of Pixii's magnet passed the coil is (2/pi)0.5 amperes and that the magnet rotate with a characteristic angular frequency ω0.

Write the mathmatical expression for the time-domain signal (current vs. time) from such AC generator. For simplicity, assume that the magnet was already spinning at the beginning of the observation and the magnet's poled happened to be just below the coils at time zero.

I am not really sure how to start, I just need know that I need something relate current with time and equation should have cosine.
Thanks for any help
 
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