Question

1. The forced response for a first-order differential equation with a constant forcing function is also referred to as the steady-state solution.

True or false

2. If the roots of the characteristic equation for a second-order circuit are real and equal, the network response is:

a. overdamped

b. underdamped

c. critically damped

3. If the response of a second-order circuit is oscillatory, the circuit is

a. underdamped

b. critically damped

c. overdamped

4. The forced response for a second-order circuit excited by a DC source is always a constant.

True or false

Answer #1

Consider the second order differential equation d2/dt^2 x + 6
dx/dt + 10x = 0. Classify the harmonic oscillator
(undamped, underdamped, critically damped, over damped). Justify
your answer.

Consider the nonlinear second-order differential
equation 4x"+4x'+2(k^2)(x^2)− 1/2 =0, where k > 0 is a constant.
Answer to the following questions.
(a) Show that there is no periodic solution in a simply connected
region R={(x,y) ∈ R2 | x <0}. (Hint: Use the corollary to
Theorem 11.5.1>>
If symply connected region R either contains no critical points of
plane autonomous system or contains a single saddle point, then
there are no periodic solutions. )
(b) Derive a plane autonomous system...

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