1550078481-Ordinary_Differential_Equations__Roberts_

296 Ordinary Differential Equations

c. Suppose damping is added to the system and the d amping constant

is computed to be c = .4 kg/s. What is the resonance frequency,

FR?

2. Suppose the equation of motion of some system satisfies the differential
   equation
   y" + cy' + 15y = 4sinw*t.

a. What value of c produces resonance?

b. If c = 4, what value of w* produces resonance?

3. In the RLC series circuit suppose the electromotive force has a constant
   value of E.

a. Find t he steady state solution for the charge on the capacitor,

qp(t).

b. What is limt_, 00 qp(t)?

c. What is limt-+oo i(t)?

4. In the RLC series circuit suppose the electromotive force is J(t)
   Esinw*t.

a. For R = 0 (an LC series circuit) and w* -j. 1 /,/LC, find t he

steady state solution for the charge on the capacitor, qp(t). What

is limt-+oo qp(t)?

b. For R = 0 and w* = 1 /,/LC, find the steady state solution for the

charge on the capacitor, qp(t). What is limt_, 00 qp(t)?

c. For L = 0 (an RC series circuit) find t he steady state solution for

the charge on the capacitor. What is limt_, 00 qp(t)?

5. Find the steady state current, ip(t), flowing in an RL series circuit

(C = 0) if

a. f(t) = E , a constant. What is limt_, 00 ip(t)?

b. f(t) =Ecosw*t.

6. Find the steady state current, ip(t), for an RLC series circuit if E(t) =
   Ecoswt. For what value of w will the amplitude of the steady state
   current be a maximum?