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Why is the kinetic energy of antinodes for a standing wave maximum when all the particals pass through their mean position?

The elastic potential energy of particals near the nodes are maximum when they are at their maximum, as they are stretched most. Thus when all the particals will pass through their mean postion, I should expect the ones near the nodes to have maximum kinetic energy as all the elastic potential energy should then have been converted to kinetic. But how can those which have minimum elastic potential energy during their maximum respective amplitude (i.e. ones near the antinode) have the maximum kinetic energy. Where did the energy came from?

If I am saying that the ones having maximum amplitude should have maximum kinetic energy at their mean position, then in turn they should be the ones having maximum potential energy at their respective extremes (ones near the antinode) but again that is not the case.

I am really confused about that!!

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