SIMPLE PENDULUM

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SIMPLE PENDULUM
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SIMPLE PENDULUM
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SIMPLE PENDULUM
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SIMPLE PENDULUM
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SIMPLE PENDULUM
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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

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ENERGY

• ½ v² gL cos q gL cos q m
• v² 2gL (cos q cos q m) and s L q

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ENERGY
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Amplitude
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Time
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Time
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NEWTON'S LAW OFUNIVERSAL GRAVITATION
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At the surface ofthe Earth
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POTENTIAL ENERGY
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POTENTIAL ENERGY

• Choose U 0 at r

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Conservation ofMechanical Energy

• When dropped from
• r R
• with v0 0.

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Conservation ofMechanical Energy