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Consider say The Girl in a Swing" (Richard Adams): if the girl is pushed at
max displacement (the way it is usually done) at the resonant frequency the
result is well known.
But suppose she is given an aiding push on the way up instead of down or at
the nadir. Would it matter? Indeed suppose she is pushed off resonant
frequency. Does that mean she can't swing at all? Her frequency won't be
at the resonant frequency, but she will swing.
Somebody give a better example. please.