Rectify a Periodic Wave 

Rectify a sine wave.

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X sol = DSolve[{x''[t] + x[t] == 0, x[0] == 0, x'[0] == 1, WhenEvent[x[t] == 0, x'[t] -> -x'[t]]}, x, {t, 0, 4 \[Pi]}]

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Plot the rectified wave along with the original sine wave.

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X {Plot[Sin[t], {t, 0, 4 \[Pi]}, Filling -> Axis, FillingStyle -> Orange], Plot[(x[t] /. sol), {t, 0, 4 \[Pi]}, Filling -> Axis, FillingStyle -> Green]}

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Rectify an elliptic wave. In this case, the event times are obtained using a numerical method.

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X sol = DSolve[{x''[t] + Sin[x[t]] == 0, x[0] == 0., x'[0] == 1, WhenEvent[x[t] == 0, x'[t] -> -x'[t]]}, x[t] , {t, 0, 10}]

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X {Plot[2 JacobiAmplitude[t/2, 4], {t, 0, 10.5}, Filling -> Axis, FillingStyle -> Orange], Plot[(x[t] /. sol), {t, 0, 10.5}, Filling -> Axis, FillingStyle -> Green]}

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