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3.8:  Mechanical and Electrical Vibrations

Electrical Vibrations:


Voltage drop across resistor:  $IR$

Voltage drop across capacitor: $Q/C$ 

Voltage drop across inductor:  $LI'$


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\centerline{$L{dI(t) \over dt} + RI(t) + {1 \over C}Q(t) = E(t), ~~L, R, C \geq 0 {\hbox{ and 
}}
I = {dQ \over dt}$~~~~~~}

$L$ = inductance (henrys),
\u
$R$ = resistance (ohms)
\u
$C$ = capacitance (farads)
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$Q(t)$ = charge at time $t$ (coulombs)
\u
$I(t)$ = current at time $t$ (amperes)
\u
$E(t)$ = impressed voltage (volts).

1 volt = 1 ohm $\cdot$ 1 ampere = 1 coulomb / 1 farad = 1 henry $\cdot$ 1 amperes/ 1 second




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