1550078481-Ordinary_Differential_Equations__Roberts_

278 Ordinary Differential Equations

The spring-mass mechanical systems ( 4) and ( 5) may be set in motion

(i) by pulling the mass downward from its equilibrium position (y(O) =

c 0 > 0) and releasing it without imparting any velocity (y' (0) = c1 = 0),

(ii) by lifting the mass upward from its equilibrium position (y(O) = co < 0)

and releasing it without imparting any velocity (y'(O) = c1 = 0), (iii) by

applying an instantaneous external force to the mass (say, by hitting the
mass from below with a hammer) and thereby imparting a velocity to the

mass (y' (0) = c 1 -=/:-0) and dislodging the mass from the equilibrium position

(y(O) = c 0 = 0), or (iv) by pulling the mass downward or lifting the mass

upward (y(O) = c 0 -=/:-0) and releasing the mass and imparting some velocity

(y'(O) = C1-=/:-0).

Electrical Circuits Now let us consider the flow of electric current in
some simple circuits. Table 6.1 contains a list of some common electric circuit
components and quantities, the alphabetic symbols usually used to denote
the numeric value of these components and quantities, the graphic symbols
used to represent components in schematic drawings, and the units associ-
ated with each component or quantity. The units of the components were
named in honor of the following physicists: Andre Marie Ampere (1775-1836,
French), Charles Augustin De Coulomb (1736-1806, French), Michael Fara-
day (1791-1867, English), Joseph Henry (1797-1878, American), Georg Simon
Ohm (1789-1854, German), and Allessandro Volta (1745-1827, Itali an).

Table 6.1 Electric circuit components and quantities

Circuit component Symbol

or

quantity Alphabetic Graphic Unit

Capacitor c -H- Farad (F)

Electric charge q Coulomb (C)

Electric current i Ampere (A)

Electromotive force

Battery E --11111--- Volt (V)

Generator Esinwt --0--- Volt (V)

Inductor L ~ Henry (H)

Resistor R -WW- Ohm (D)

Time t Seconds (s)