2. For each ODE below, do the following: i. Give one value of k (from the given possibilities) for which the ODE exhibits resonance. ii. Give one value of k (from the given possibilities) for which the ODE does not exhibit resonance, and find a particular solution in that case. (a) x" + kx = cos(2t), with these possible values of k for you to choose from: 0, 1, 2, 3, or 4.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.2: Trigonometric Functions Of Angles
Problem 29E
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2.
For each ODE below, do the following:
i. Give one value of k (from the given possibilities) for which the ODE exhibits resonance.
ii. Give one value of k (from the given possibilities) for which the ODE does not exhibit resonance,
and find a particular solution in that case.
(a) x" + kx = cos(2t), with these possible values of k for you to choose from: 0, 1, 2, 3, or 4.
(b) x" + kx = 2t, with these possible values of k for you to choose from: 0, 1, 2, 3, or 4.
Careful! Did you answer both questions i and ii, for both ODES?
Transcribed Image Text:2. For each ODE below, do the following: i. Give one value of k (from the given possibilities) for which the ODE exhibits resonance. ii. Give one value of k (from the given possibilities) for which the ODE does not exhibit resonance, and find a particular solution in that case. (a) x" + kx = cos(2t), with these possible values of k for you to choose from: 0, 1, 2, 3, or 4. (b) x" + kx = 2t, with these possible values of k for you to choose from: 0, 1, 2, 3, or 4. Careful! Did you answer both questions i and ii, for both ODES?
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