Solved
As we can see the approach using “root” by providing the interval 0s to 0.15s does not always give us the first of all zeros (see n=1).
If you intended to calculate the first occurrence you might be better off with using the “root” function by providing a guess value (here I used t=0s as a guess. As we don’t k now the algorithm used by “root” there is no guarantee that doing so will always give us the first positive root, but in case of your function this seems to be the case and we even also get a solution for n=4 (which is way above the 0.1s you had chosen for the upper limit in your plot.

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