Spring Mass Systems

Consider a spring-mass system consisting of three masses

m1:=plot::Rectangle(-3..0, -1..1, Filled = TRUE, Color = RGB::Blue,FillColor = RGB::Red,Title="Mass 1",TitlePosition=[-1.5,0],FillPattern=Solid)
plot::Rectangle(-3..0, -1..1)
m2:=plot::Rectangle(3..6, -1..1, Filled = TRUE, Color = RGB::Blue, FillColor = RGB::Red,Title="Mass 2",TitlePosition=[4.5,0],FillPattern=Solid) m3:=plot::Rectangle(9..12, -1..1, Filled = TRUE, Color = RGB::Blue, FillColor = RGB::Red,Title="Mass 3",TitlePosition=[10.5,0],FillPattern=Solid) k1:=.55*sin(8.5*t),t=0..3, Color= RGB::Red k2:=.55*sin(8.5*x),x=-6..-3 k3:=.55*sin(8.4*y),y=6..9, Color= RGB::Red k4:=.55*sin(8.4*z),z=12..15, LineColorType = Monochrome baseleft:=plot::Rectangle(-7..-6, -1.75.. 1.5, Filled = TRUE, Color = RGB::Black, FillColor = RGB::Black,FillPattern=Solid) baseright:=plot::Rectangle(15..16, -1.75.. 1.5, Filled = TRUE, Color = RGB::Black, FillColor = RGB::Black,FillPattern=Solid) base:=plot::Rectangle(-6..15, -1.75.. -1.25, Filled = TRUE, Color = RGB::Black, FillColor = RGB::Black,FillPattern=Solid) circle1:=plot::Circle2d(.125, [-2.5,-1.125],Filled=TRUE,Title="Spring 1",TitlePosition=[-4.5,.75]) circle2:=plot::Circle2d(.125, [-.5,-1.125],Filled=TRUE,Title="Spring 2",TitlePosition=[1.5,.75]) circle3:=plot::Circle2d(.125, [3.5,-1.125],Filled=TRUE,Title="Spring 3",TitlePosition=[7.5,.75]) circle4:=plot::Circle2d(.125, [5.5,-1.125],Filled=TRUE,Title="Spring 4",TitlePosition=[13.5,.75]) circle5:=plot::Circle2d(.125, [9.5,-1.125],Filled=TRUE) circle6:=plot::Circle2d(.125, [11.5,-1.125],Filled=TRUE) line1:=plot::Line2d([-2.5,1],[-2.5,2],LineColor=RGB::Black) line2:=plot::Arrow2d([-2.5,2],[-2,2],LineColor=RGB::Black,Title="X1",TitlePosition=[-1.6,1.95]) line3:=plot::Line2d([3.5,1],[3.5,2],LineColor=RGB::Black) line4:=plot::Arrow2d([3.5,2],[4,2],LineColor=RGB::Black,Title="X2",TitlePosition=[4.4,1.95]) line5:=plot::Line2d([9.5,1],[9.5,2],LineColor=RGB::Black) line6:=plot::Arrow2d([9.5,2],[10,2],LineColor=RGB::Black,Title="X3",TitlePosition=[10.4,1.95]) plot(m1,m2,k1,k2,k3,m3,k4,baseleft,baseright, base,circle1,circle2,circle3,circle4,circle5,circle6,line1,line2,line3,line4,line5,line6 ,GridVisible= FALSE, AxesVisible= FALSE, Width = 18*unit::inch, Height = 4*unit::inch,Header="Horizontal Spring Mass System with 6 Degrees of Freedom")

This tutorial contains many MuPAD scripts. You, as the user, are free to use all codes for your needs, and have the right to distribute this tutorial and refer to this tutorial as long as this tutorial is accredited appropriately. Any comments and/or contributions for this tutorial are welcome; you can send your remarks to <Vladimir_Dobrushkin@brown.edu>