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 q m)
mg(L – L cos q m) = ½ mv²
+ mg(L – L cos q )
– gL cos q m = ½ v² – gL cos q

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

8. ENERGY

9. Amplitude

10. Time

11. Time

12. NEWTON'S LAW OF UNIVERSAL GRAVITATION

13. At the surface of the Earth

14. POTENTIAL ENERGY

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

16. Conservation of Mechanical Energy
When dropped from
r = R
with v0 = 0.

17. Conservation of Mechanical Energy