1550078481-Ordinary_Differential_Equations__Roberts_

Applications of Linear Equations with Constant Coefficients 283 angle is usually chosen with the restriction -n < ¢ :S n. Wit ...

284 Ordinary Differential Equations motion the solution (19) may be rewritten in the equivalent form (20) y(t) = Ae-at sin (wt+¢ ...

Applications of Linear Equations with Constant Coefficients 285 Since r 1 < 0 and r2 < 0, both er,t and er^2 t are monoton ...

286 Ordinary Differential Equations The roots of the auxiliary equation, mr^2 + k = 0, are r 1 = ../klffii = wi and r 2 = -../kl ...

Applications of Linear Equations with Constant Coefficients 287 EXAMPLE 2 Equation of Motion of a Damped Mass on a Spring A. l k ...

288 Ordinary Differential Equations EXAMPLE 3 Finding the Equation for the Charge on a Capacitor Find the equation for the charg ...

Applications of Linear Equations with Constant Coefficients 289 EXERCISES 6.1.1 Exercises 1-9 pertain to simple pendulums. In th ...

290 Ordinary Differential Equations c. What is the phase angle? A damped p endulum of length .6 m with a bob of mass .5 kg is ...

Applications of Linear Equations with Constant Coefficients 291 When a 1 kg mass is attached to a certain spring and the system ...

292 Ordinary Differential Equations 6.1.2 Forced Motion Suppose some mechanical or electrical system whose state is represented ...

Applications of Linear Equations with Constant Coefficients 293 Since the set {sinw*t, cosw*t} is a linearly independent set, we ...

294 Ordinary Differential Equations where a= b/(2a), w = v'4ad-b^2 /(2a), and A , B, C , and</> are arbitrary constant s. ...

Applications of Linear Equations with Constant Coefficients 295 a sufficiently long period of time the solution depends only on ...

296 Ordinary Differential Equations c. Suppose damping is added to the system and the d amping constant is computed to be c = .4 ...

Applications of L inear Equations with Constant Coefficients 297 6.2 Higher Order Differential Equations In this section we will ...

298 Ordinary Differential Equations spring-mass system satisfy the linear system of differential equations (28a) (28b) Solving e ...

Applications of Linear Equations with Constant Coefficients 299 System at Equilibrium System at Timet Figure 6.8 A Coupled Sprin ...

300 Ordinary Differential Equations (33a) (33b) where g is the constant of gravitational acceleration. I ~ I I Y2 I. I 1 vertica ...

Applications of Linear Equations with Constant Coefficients 301 (34a) x" = -HRy' +ER (34b) y" = HRx' where H is the intensity of ...

302 Ordinary Differential Equations to flow from one compartment to another is negligible, and the fluid in each compartment has ...