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SIMPLE PENDULUM

SIMPLE PENDULUM. SIMPLE PENDULUM. SIMPLE PENDULUM. SIMPLE PENDULUM. SIMPLE PENDULUM. ENERGY. U = mgy = mg ( L – L cos q ) E = K + U = ½ mv ² + mg ( L – L cos q ) E = mg ( L – L cos q m ) mg ( L – L cos q m ) = ½ mv ²

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SIMPLE PENDULUM

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  1. SIMPLE PENDULUM

  2. SIMPLE PENDULUM

  3. SIMPLE PENDULUM

  4. SIMPLE PENDULUM

  5. SIMPLE PENDULUM

  6. ENERGY • U = mgy = mg(L – L cos q) • E = K + U =½ mv² + mg(L – L cos q) • E = mg(L – L cos qm) • mg(L – L cos qm) =½ mv² • + mg(L – L cos q) • – gL cos qm =½ v² – gL cos q

  7. ENERGY • ½ v² = gL cos q – gL cos qm • v² = 2gL (cos q – cos qm) and s = L q

  8. ENERGY

  9. Amplitude

  10. Time

  11. Time

  12. NEWTON'S LAW OFUNIVERSAL GRAVITATION

  13. At the surface ofthe Earth

  14. POTENTIAL ENERGY

  15. POTENTIAL ENERGY • Choose U = 0 at r = ¥

  16. Conservation ofMechanical Energy • When dropped from • r = R • with v0 = 0.

  17. Conservation ofMechanical Energy

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