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In Sympy solve the initial value problem for a damped harmonic oscillator my" + cy' + ky = g(t), y(0) = 0.05, y' (0) = 0. for m = 2, k = 30, c = 0.6 and g = 0. Plot the resulting solution for t€ (0, 30), and classify the motion as underdamped, critically damped, or overdamped. Repeat with the same values of m, k, c, but with g(t) changed to: (a) g(t) 4 cos(2t) (b) g(t) = 4 cos(4t) (c) g(t) = 4 cos(6t) Which gives the largest amplitude?

In Sympy solve the initial value problem for a damped harmonic oscillator my" + cy' + ky = g(t), y(0) = 0.05, y' (0) = 0. for m = 2, k = 30, c = 0.6 and g = 0. Plot the resulting solution for t€ (0, 30), and classify the motion as underdamped, critically damped, or overdamped. Repeat with the same values of m, k, c, but with g(t) changed to: (a) g(t) 4 cos(2t) (b) g(t) = 4 cos(4t) (c) g(t) = 4 cos(6t) Which gives the largest amplitude?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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5) In Sympy solve the initial value problem for a damped harmonic oscillator my" + cy' + ky = g(t), y(0) = 0.05, y'(0) = 0. for m = 2, k = 30, c = 0.6 and g = 0. Plot the resulting solution for t € (0, 30), and classify the motion as underdamped, critically damped, or overdamped. Repeat with the same values of m, k, c, but with g(t) changed to: (a) g(t) = 4 cos(2t) (b) g(t) = 4 cos(4t) (c) g(t) = 4 cos(6t) Which gives the largest amplitude?
Transcribed Image Text:5) In Sympy solve the initial value problem for a damped harmonic oscillator my" + cy' + ky = g(t), y(0) = 0.05, y'(0) = 0. for m = 2, k = 30, c = 0.6 and g = 0. Plot the resulting solution for t € (0, 30), and classify the motion as underdamped, critically damped, or overdamped. Repeat with the same values of m, k, c, but with g(t) changed to: (a) g(t) = 4 cos(2t) (b) g(t) = 4 cos(4t) (c) g(t) = 4 cos(6t) Which gives the largest amplitude?
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