The mass-spring system is described by the equationy" = -3y – cy';c > 0 is the drag coefficient.(a) For c = 2, find the solution with initial conditions y(0) = 0, y' (0) = 1. Show that the system will oscillate near the equilibrium (i.e. y willchange its sign infinitely many times).(b) For c = 4, find the solution with initial conditions y(0) = 0, y' (0) = 1. Show that y(t) will be positive for all t > 0 and will tend to theequilibrium y = 0 as t → +o.

We find the general solution of given differential equation in(a) and (b) and show the results as…

The mass-spring system is described by the equation y" = -3y – cy/'; :> 0 is the drag coefficient. a) For c = 2, find the solution with initial conditions y(0) = 0, y' (0) = 1. Show that the system will oscillate near the equilibrium (.e. y will change its sign infinitely many times). b) For c = 4, find the solution with initial conditions y(0) = 0, y' (0) = 1. Show that y(t) will be positive for all t > 0 and will tend to the equilibrium y = 0 as t → +o.

The mass-spring system is described by the equation y" = -3y – cy/'; :> 0 is the drag coefficient. a) For c = 2, find the solution with initial conditions y(0) = 0, y' (0) = 1. Show that the system will oscillate near the equilibrium (.e. y will change its sign infinitely many times). b) For c = 4, find the solution with initial conditions y(0) = 0, y' (0) = 1. Show that y(t) will be positive for all t > 0 and will tend to the equilibrium y = 0 as t → +o.

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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