The mass-spring system is described by the equation y" = -3y – cy'; > 0 is the drag coefficient. ) 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 ange its sign infinitely many times).
The mass-spring system is described by the equation y" = -3y – cy'; > 0 is the drag coefficient. ) 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 ange its sign infinitely many times).
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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 ocillate 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) willI be positive for all t > 0 and will tend to the
equilibrium y = 0 as t → +00.
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