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(a) Find the general solution of the motion of a mass attached to the ceiling by a spring in presence of friction, i.e. solve the ODE mÿj = mg - k(yl) - vý. with m = 1, k = 3, y = 2, g = 10, 1 = 5, where y indicates the distance of the mass from the ceiling. (b) What is the limit lim+→∞ y(t) for the motion of the mass described in (a)? Describe in words the asymptotic dynamical behaviour of the mass for t→∞. (c) Determine whether the differential equation 1 2₁ is exact. If it is exact, find its general solution in explicit form. + y cos(x) + (yx + sin(x) - e") y' = 0

(a) Find the general solution of the motion of a mass attached to the ceiling by a spring in presence of friction, i.e. solve the ODE mÿj = mg - k(yl) - vý. with m = 1, k = 3, y = 2, g = 10, 1 = 5, where y indicates the distance of the mass from the ceiling. (b) What is the limit lim+→∞ y(t) for the motion of the mass described in (a)? Describe in words the asymptotic dynamical behaviour of the mass for t→∞. (c) Determine whether the differential equation 1 2₁ is exact. If it is exact, find its general solution in explicit form. + y cos(x) + (yx + sin(x) - e") y' = 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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(a) Find the general solution of the motion of a mass attached to the ceiling by a spring in presence of friction, i.e. solve the ODE mij = mg - k(y - 1) - vý. with m = 1, k3, y = 2, g = 10, 1 = 5, where y indicates the distance of the mass from the ceiling. (b) What is the limit limt→∞ y(t) for the motion of the mass described in (a)? Describe in words the asymptotic dynamical behaviour of the mass for t→∞0. (c) Determine whether the differential equation 1 2 2 + y cos(x) + (yx + sin(x) — e²) y' = 0 is exact. If it is exact, find its general solution in explicit form.
Transcribed Image Text:(a) Find the general solution of the motion of a mass attached to the ceiling by a spring in presence of friction, i.e. solve the ODE mij = mg - k(y - 1) - vý. with m = 1, k3, y = 2, g = 10, 1 = 5, where y indicates the distance of the mass from the ceiling. (b) What is the limit limt→∞ y(t) for the motion of the mass described in (a)? Describe in words the asymptotic dynamical behaviour of the mass for t→∞0. (c) Determine whether the differential equation 1 2 2 + y cos(x) + (yx + sin(x) — e²) y' = 0 is exact. If it is exact, find its general solution in explicit form.
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