# Differential Equations and Harmonic Oscillators

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In Exercises 21?28, consider harmonic oscillators with mass in, spring constant k, and damping coefficient b. (The values of these parameters match up with those in Exercises 13?20). For the values specified,

(a) find the general solution of the second-order equation that models the motion of the oscillator;

(b) find the particular solution for the given initial condition; and

(c) using the equations for the solution of the initial-value problem, sketch the y(t)and v(t)-graphs. Compare these graphs to your sketches for the corresponding exercise from Exercises 13?20.

21. rn = 1, k = 7, b = 8, with initial conditions y(O) = ?1, v(0) = 5

22. m = 1, k = 8, b = 6, with initial conditions y(O) = 1, v(0) = 0

23. m = 1, k = 5, b = 4, with initial conditions y(O) = 1, v(0) = 0

24. m = 1, k = 8, b = 0, with initial conditions y(0) = 1, v(0) = 4

Please solve for only #24. In part (c), you do not need to draw the graph, but if you do, I will appreciate it. No need for comparison, too..

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Differential equations and harmonic oscillators are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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Please solve for only #24. In part (c), you do not need to draw the graph, but if you do, I will appreciate it. No need for comparison, too..

Thank ...

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