Apple Newton Works Graphing Calculator Manuale Utente Scaricare il pdf (Pagina 26)

A 32-lb. weight is attached to the lower end of a coil spring suspended from the

ceiling. The weight comes to rest in its equilibrium position, stretching the spring

2 ft. The weight is then pulled down 5 in. below its equilibrium position and released

at t = 0. No external forces are present; but the resistance of the medium in pounds

is equal to 4(dx/dt), where dx/dt is the instantaneous velocity in feet per second. Plot

the damped oscillatory motion.

Using the above information with the basic differential equation for free,

damped motion:

m * d

x/dt

+ a * dx/dt + k * x = 0

Solving for the root and differentiating with respect to t, the solution is:

x = sqrt(3)/3 * e^(–2t) * cos(2sqrt(3) * t – π/6)

26 Chapter 2

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Apple Newton Works Graphing Calculator Manuale Utente Pagina 26