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Periodic Motion

Periodic Motion. Recall that. Using the fact that the maximum displacement is A , the work energy theorem states. Solving for the velocity, get. Using the solution for position, the velocity becomes. Graphical Interpretation. Importance of Periodic Motion.

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Periodic Motion

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  1. Periodic Motion • Recall that • Using the fact that the maximum displacement is A, the work energy theorem states

  2. Solving for the velocity, get • Using the solution for position, the velocity becomes

  3. Graphical Interpretation

  4. Importance of Periodic Motion • All atomic and molecular bonds can be approximated by springs • All signals can be decomposed into sets of periodic motions • Non periodic motion can also be decomposed into sets of periodic motions

  5. Simple Pendulum • Newton’s second law yields

  6. For small angles, sinq ~ q • Recall that q = x/r, a = a/r, so • Comparing with Hooke’s Law, see that

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