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Yes, the velocity of the chair changes as a simple harmonic motion (SHM) and varies from 0 to maximum back to 0 back to ... The acceleration of the chair also relates to SHM in that it varies inversely with the velocity - high velocity = 0 acceleration, 0 velocity = maximum acceleration. If you chart the speed of the shadow of the chair you will see a smooth waveform - likely a sine wave.

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Q: Is a rocking chair related to periodic events?
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