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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
Periodic Motion
  • Recall that
  • Using the fact that the maximum displacement is A, the work energy theorem states
slide2
Solving for the velocity, get
  • Using the solution for position, the velocity becomes
importance of periodic motion
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
simple pendulum
Simple Pendulum
  • Newton’s second law yields
slide6
For small angles, sinq ~ q
  • Recall that q = x/r, a = a/r, so
  • Comparing with Hooke’s Law, see that