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(8) The equation my" +cy' + ky = F describes the motion of a mass m attached to a spring with spring constant k with frication propor- tional to the velocity and external force F acting on the mass. Let A and are real numbers and let m, k > 0, c≥ 0 be so that 4km - c² > 0. Prove that y = Ae2mt sin (√ k c2 t+o m 4m² satisfies my" +cy' + ky = 0.

(8) The equation my" +cy' + ky = F describes the motion of a mass m attached to a spring with spring constant k with frication propor- tional to the velocity and external force F acting on the mass. Let A and are real numbers and let m, k > 0, c≥ 0 be so that 4km - c² > 0. Prove that y = Ae2mt sin (√ k c2 t+o m 4m² satisfies my" +cy' + ky = 0.

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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(8) The equation my" +cy' + ky = F describes the motion of a mass m attached to a spring with spring constant k with frication propor- tional to the velocity and external force F acting on the mass. Let A and are real numbers and let m, k > 0, c≥ 0 be so that 4km - c² > 0. Prove that y = Ae2mt sin (√ k c2 t+o m 4m² satisfies my" +cy' + ky = 0.
Transcribed Image Text:(8) The equation my" +cy' + ky = F describes the motion of a mass m attached to a spring with spring constant k with frication propor- tional to the velocity and external force F acting on the mass. Let A and are real numbers and let m, k > 0, c≥ 0 be so that 4km - c² > 0. Prove that y = Ae2mt sin (√ k c2 t+o m 4m² satisfies my" +cy' + ky = 0.
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