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
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Chapter2: Second-order Linear Odes
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The mass-spring system is described by the equation
y" = -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 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.
Transcribed Image Text:The mass-spring system is described by the equation y" = -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 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.
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