Unformatted text preview: • Capacitor has an electric ﬁeld created by the charge built up on the top/bottom plates (equal/opposite) • The voltage drop is proportional to the charge: V = q/C • Sum of the voltages must be 0 (Kirchoff, Germany 1845): L ¨ q + q/C = 0 • The solution of ¨ q + ω 2 q = 0 is well known to us, but in this case ω = 1 / √ LC • Total energy: 1 2 LI 2 + 1 2 q 2 /C where the ﬁrst term is magnetic inertia (kinetic) and the second term is electric potential (springlike) Mass/Spring LC circuit x q F V m L s 1/C 5. Other systems • a) Pendulum: ml ¨ θ + mgθ = 0 and ω = p g/l • b) Torsion Oscillator: I ¨ θ + cθ = 0 and ω = p c/I • e) Water Utube: ρl ¨ x + 2 gρx = 0 and ω = p 2 g/l • g) Bobber in ﬂuid Torsion: m ¨ x + Agρx = 0 and ω = p AGρ/m • d) Mass on a tensioned string: m ¨ x + 2 Tx/l = 0 and ω = p 2 T/lm...
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 Fall '07
 PierreSavaria
 mechanics, Energy, Mass, Statistical Mechanics, Inductor, phase space

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