PHYS 422 Lecture 13 Free Vibrations II

PHYS 422 Lecture 13 Free Vibrations II - Free Vibrations of...

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Free Vibrations of Physical Systems II
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Pendula Si l P d l O Simple Pendulum θ l l – 2D problem though expressible through the single parameter θ l-y through the single parameter – exchange of KE and PE during the motion P m N – consider θ small y << x 2 2 x y l x y – conservation of energy 2 1 mv mgy E + 2 2 2 2 dx dy = + v dt dt =
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Pendula Simple Pendulum O – use the fact y << x 2 2 1 1 dx mg E θ l-y l 2 2 m x dt l g + = – use the angular displacement instead l ω = P y m N d v l dt θ = x 2 2 1 (1 cos ) 2 1 1 y l l d θ θ θ = 2 2 2 2 ml mgl E dt θ + =
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