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In Exercises 21-28, consider harmonic oscillators with mass m, spring constant k, and damping coefficient b. (The values of these parameters match up with those in Exer- cises 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 (e) using the equations for the solution of the initial-value problem, sketch the y(t)- and v()-graphs. Compare these graphs to your sketches for the corresponding ex- ercise from Exercises 13-20. 21. m = 1, k = 7, b = 8, with initial conditions y(0) = -1, v(0) = 5 22. m = 1, k=8, b = 6, with initial conditions y(0) = 1, v(0) = 0 23. m = 1, k = 5, b=4, with initial conditions y(0) = 1, v(0) = 0 24. m = 1, k-8, b = 0, with initial conditions y(0) = 1, v(0) = 4 25. m = 2, k = 1, b = 3, with initial conditions y(0) = 0, v(0) = 3

In Exercises 21-28, consider harmonic oscillators with mass m, spring constant k, and damping coefficient b. (The values of these parameters match up with those in Exer- cises 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 (e) using the equations for the solution of the initial-value problem, sketch the y(t)- and v()-graphs. Compare these graphs to your sketches for the corresponding ex- ercise from Exercises 13-20. 21. m = 1, k = 7, b = 8, with initial conditions y(0) = -1, v(0) = 5 22. m = 1, k=8, b = 6, with initial conditions y(0) = 1, v(0) = 0 23. m = 1, k = 5, b=4, with initial conditions y(0) = 1, v(0) = 0 24. m = 1, k-8, b = 0, with initial conditions y(0) = 1, v(0) = 4 25. m = 2, k = 1, b = 3, with initial conditions y(0) = 0, v(0) = 3

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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In Exercises 21-28, consider harmonic oscillators with mass m, spring constant k, and damping coefficient b. (The values of these parameters match up with those in Exer- cises 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 ex- ercise from Exercises 13-20. 21. m = 1, k = 7, b = 8, with initial conditions y(0) = -1, v(0) = 5 22. m = 1, k = 8, b = 6, with initial conditions y(0) = 1, v(0) = 0 23. m = 1, k = 5, b = 4, with initial conditions y(0) = 1, v(0) = 0 24. m = 1, k = 8, b = 0, with initial conditions y(0) = 1, v(0) = 4 25. m = 2, k = 1, b = 3, with initial conditions y(0) = 0, v (0) = 3 26. m = 9, k = 1, b = 6, with initial conditions y(0) = 1, v(0) = 1 27. m = 2, k = 3, b = 0, with initial conditions y(0) = 2, v(0) = -3 28. m = 2, k = 3, b = 1, with initial conditions y(0) = 0, v(0) = -3
Transcribed Image Text:In Exercises 21-28, consider harmonic oscillators with mass m, spring constant k, and damping coefficient b. (The values of these parameters match up with those in Exer- cises 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 ex- ercise from Exercises 13-20. 21. m = 1, k = 7, b = 8, with initial conditions y(0) = -1, v(0) = 5 22. m = 1, k = 8, b = 6, with initial conditions y(0) = 1, v(0) = 0 23. m = 1, k = 5, b = 4, with initial conditions y(0) = 1, v(0) = 0 24. m = 1, k = 8, b = 0, with initial conditions y(0) = 1, v(0) = 4 25. m = 2, k = 1, b = 3, with initial conditions y(0) = 0, v (0) = 3 26. m = 9, k = 1, b = 6, with initial conditions y(0) = 1, v(0) = 1 27. m = 2, k = 3, b = 0, with initial conditions y(0) = 2, v(0) = -3 28. m = 2, k = 3, b = 1, with initial conditions y(0) = 0, v(0) = -3
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