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Unformatted text preview: The Mass-Spring System Math 308 This Maple session uses the mass-spring system to demonstrate the phase plane, direction fields, solution curves (``trajectories''), the extended phase space, and more. The differential equation is = + + m & 2 t 2 ( ) y t b & t ( ) y t k ( ) y t (I've used b instead of the usual for the coefficient of friction.) We convert this to a system by defining = ( ) v t t ( ) y t Then = t ( ) v t-- k ( ) y t m b & t ( ) y t m or = t ( ) v t-- k ( ) y t m b ( ) v t m This equation along with the equation that defines v(t) make up a system of two equations. > with(DEtools): We first define the two equations that make up the system: > eq1 := diff(y(t),t) = v(t); := eq1 = t ( ) y t ( ) v t > eq2 := diff(v(t),t) = -(k/m)*y(t)-(b/m)*v(t); := eq2 = t ( ) v t-- k ( ) y t m b ( ) v t m Now define a variable that holds the system: > sys := [eq1,eq2]; :=...
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This note was uploaded on 02/11/2012 for the course MTH 141, 142, taught by Professor Mcallister during the Spring '08 term at SUNY Empire State.
- Spring '08