There is a little program of mine, it's about Harmonic_oscillator

For more Information about Harmonic_oscillator you can take a look at Wikipedia

http://en.wikipedia.org/wiki/Harmonic_oscillator

Screenshot: 

[https://lh5.googleusercontent.com/-X8ZhjxaCX70/UWcEFYJIltI/AAAAAAAAB1g/N5N0B-NE9U8/w497-h373/1.png]



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    package require Tk
    wm withdraw .
    wm title . "Harmonic oscillator ver 1.01 - sicheng6699@gmail.com"
        wm minsize . 300 200

    global GB
        set GB(screenwidth) [winfo screenwidth .]
        set GB(screenheight) [winfo screenheight .]

#Oben
    pack [frame .ft -bd 2 -relief groov ] -side top  -fill both -ipadx 2 -ipady 2 -padx 2 -pady 2
    pack [frame .ft.f1 ] -side left  -fill both -expand 1
    pack [frame .ft.f2 ] -side left
    pack [label .ft.f1.titel -text "Harmonic oscillator" -font {Arial 20}]
    pack [button .ft.f2.help  -text "Help" -command {tk_messageBox -message "Author: Lei ZHOU \n Last change: 11.04.2013"}] -side right -padx 10

#Unten
    pack [frame .fu -bd 2 -relief groov ] -side bottom  -fill both -ipadx 2 -ipady 2 -padx 2 -pady 2
    pack [frame .fu.ok -bd 0  -relief solid ] -side left  -fill both
    pack [button .fu.ok.button -text "Start" -width 8 -font {Arial 14} -command start ] -side left  -padx 10
    pack [frame .fu.sep1 -bd 2 -relief raised -height 50 -width 3 ] -side left  -padx 10
    pack [frame .fu.m -bd 0  -relief solid ] -side top  -fill both
    pack [frame .fu.k -bd 0  -relief solid ] -side top  -fill both
    pack [frame .fu.c -bd 0  -relief solid ] -side top  -fill both
    pack [label .fu.m.b -text "Mass:"                    -width 12  -font {Arial 10} -justify right ] -side left
    pack [label .fu.k.b -text "Stiffness:"   -width 12  -font {Arial 10} -justify right ] -side left
    pack [label .fu.c.b -text "Damping:" -width 12  -font {Arial 10} -justify right ] -side left
    pack [entry .fu.m.e -textvar GB(m) -width 10  -font {Arial 10} -bd 2 ] -side left -pady 2
    pack [entry .fu.k.e -textvar GB(k) -width 10  -font {Arial 10} -bd 2 ] -side left -pady 2
    pack [entry .fu.c.e -textvar GB(c) -width 10  -font {Arial 10} -bd 2 ] -side left -pady 2

#Canvas
    pack [frame .f -bd 2 -relief sunken] -fill both -expand 1
    pack [canvas .f.c -bg white -cursor plus -highlightthickness 0  -bd 0 -width 500 -height 300] -side top -fill both  -expand 1

        wm deiconify .
        update
        set GB(width) [winfo width .]
        set GB(height) [winfo height .]
        wm geom . +[expr ($GB(screenwidth)-$GB(width))/2]-[expr ($GB(screenheight)-$GB(height))/2]
        focus -force .
        bind . <Escape>         { exit}
        #bind . <Escape>         { eval [list exec wish85 $argv0] $argv &; exit}
    bind .f.c <Expose>  { view_init }
    bind . <Return>  { start }
        bind . <F1>          { console show }

        set GB(m) 1.0
        set GB(k) 100
        set GB(c) 0.0
        set GB(start) 0
    set GB(omg) 0.0
    set GB(frq) 0.0
    set GB(prd) 0.0
    set GB(ckr) 0.0
    set GB(np) 5
    set GB(nt) [expr $GB(np)*32]
    set ux(0) 0.0
    set GB(w) [winfo width .f.c]
    set GB(h) [winfo height .f.c]
    set GB(r) 0
    set GB(x0) 0
    set GB(y0) 0
    set GB(x1) 0
    set GB(y1) 0
    set GB(id_masse) 0
    set GB(id_stab) 0
    set GB(id_kurve) 0
#########################################
    proc view_init {} {
            global GB
        set GB(start) 0
        .fu.ok.button conf -text "Start" -foreground  black
        .fu.m.e conf -state normal
        .fu.k.e conf -state normal
        .fu.c.e conf -state normal

        set GB(w) [winfo width .f.c]
                set GB(h) [winfo height .f.c]
            set GB(r) [expr $GB(h)*0.03]
            set GB(x0) [expr $GB(h)*0.8]
            set GB(y0) [expr $GB(h)*0.5]
            set GB(x1) [expr $GB(h)*0.4]
            set GB(y1) [expr $GB(h)*0.2]

        view_range
        view_masse
        view_koord
    }


    proc start {} {
            global GB ux kx ky
            #check
        .fu.m.e conf -bg white
        .fu.k.e conf -bg white
        .fu.c.e conf -bg white
        if ![string length $GB(m)]        { .fu.m.e conf -bg red ; return }
        if ![string length $GB(k)]        { .fu.k.e conf -bg red ; return }
        if ![string length $GB(c)]        { .fu.c.e conf -bg red ; return }
        if [catch {expr $GB(m)}]         { .fu.m.e conf -bg red ; return }
        if [catch {expr $GB(k)}]         { .fu.k.e conf -bg red ; return }
        if [catch {expr $GB(c)}]         { .fu.c.e conf -bg red ; return }
        if $GB(m)<=1.0e-6  { .fu.m.e conf -bg red ; return }
        if $GB(k)<=1.0e-6  { .fu.k.e conf -bg red ; return }
        if $GB(c)>$GB(ckr) {
                .fu.c.e conf -bg red ; tk_messageBox -message "The Damping should be smaller than the critical damping!" ; return }
        .fu.m.e conf -bg white
        .fu.k.e conf -bg white
        .fu.c.e conf -bg white
            #start
            if $GB(start)==1 { view_init ; return }

        set GB(start) 1
        .fu.ok.button conf -text "Stop" -foreground  red
        .fu.m.e conf -state disabled
        .fu.k.e conf -state disabled
        .fu.c.e conf -state disabled

            set GB(w) [winfo width .f.c]
                set GB(h) [winfo height .f.c]
            set GB(r) [expr $GB(h)*0.03]
            set GB(x0) [expr $GB(h)*0.8]
            set GB(y0) [expr $GB(h)*0.5]
            set GB(x1) [expr $GB(h)*0.4]
            set GB(y1) [expr $GB(h)*0.2]

            # rechnen
            global ux
            set GB(omg) [expr sqrt($GB(k)/$GB(m))]
            set GB(frq) [expr $GB(omg)/2.0/3.14159265]
            set GB(prd) [expr 1.0/$GB(frq)]
            set GB(ckr) [expr 2.0*$GB(m)*$GB(omg)]
            set dauer [expr $GB(prd)*$GB(np)]
            set dt [expr int($dauer/$GB(nt)*1000)]
            set t 0.0
            for {set i 1} {$i<=$GB(nt)} {incr i} {
                    set kxi [expr $i*1.0/$GB(nt)]
                    set t [expr $dauer*$kxi]
                    set u [expr exp( -$GB(c)/(2.0*$GB(m))*$t) *cos( ($GB(omg)*sqrt(1.0-($GB(c)/(2*$GB(m)*$GB(omg)))*($GB(c)/(2*$GB(m)*$GB(omg))) ))*$t  ) ]
                    set ux($i) [expr $GB(x1)+$u*$GB(r)*10.0]
                    set kx($i) [dx $kxi]
                    set ky($i) [dy $u]
                    set mx1($i) [expr $ux($i)-$GB(r)]
                    set mx2($i) [expr $ux($i)+$GB(r)]
            }


                while $GB(start)==1 {
            view_range
            view_masse
            view_koord
            view_titel

            for {set i 1} {$i<=$GB(nt)} {incr i} {
                if $GB(start)==0 { view_init ; return }
                .f.c delete [.f.c find withtag tobedeleted]
                .f.c create text [expr 20] [expr $GB(h)-20] -text "[expr int(100*$i/$GB(nt))]\%" -tag tobedeleted -anchor sw

                foreach {x1 y1 x2 y2} [.f.c coords $GB(id_masse)] break
                .f.c coords $GB(id_kurve) [concat [.f.c coords $GB(id_kurve)] $kx($i) $ky($i)]
                .f.c coords $GB(id_masse) [lreplace [.f.c coords $GB(id_masse)] 0 3 $mx1($i) $y1 $mx2($i) $y2]
                .f.c coords $GB(id_stab)  [lreplace [.f.c coords $GB(id_stab)] 0 0 $ux($i)]
                update
                after $dt
            }
            }
    }

    proc view_range {} {
            global GB
                .f.c delete all
                .f.c create rect 0 0 [expr $GB(w)-1] [expr $GB(h)-1] -fill "" -width 0
    }

####################################
        global GB(id_masse) GB(id_stab)
    proc view_masse { } {
            global GB
            set r $GB(r)
            set h [expr $GB(h)*0.6]
            set x $GB(x1)
            set y $GB(y1)
        set GB(id_masse) [.f.c create oval  [expr $x-$r] [expr $y-$r] [expr $x+$r]  [expr $y+$r] -fill black ]

        set x1 $x
        set y1 [expr $y+$h/2.0]
        set x2 $x
        set y2 [expr $y+$h]
        set GB(id_stab)  [.f.c create line  $x $y $x1 $y1 $x2 $y2 -fill black -width 2 -smooth 1]
        #Lager
        set x1 [expr $x2-$h/10.0]
        set y1 [expr $y2]
        set x2 [expr $x2+$h/10.0]
        set y2 [expr $y2]
        .f.c create line $x1 $y1 $x2 $y2 -fill black -width 2
    }

####################################
    proc dx {x} { return [expr $::GB(x0)+$x*$::GB(h)*0.8] }
    proc dy {y} { return [expr $::GB(y0)-$y*$::GB(h)*0.3]}
    proc view_koord {} {
            global GB
            set x0 [expr $GB(x0)]
            set y0 [expr $GB(y0)]
            set h [expr $GB(h)*0.4]
                #X-achse
                set x1 [expr $x0]
                set y1 [expr $y0]
                set x2 [expr $x0+$h*2]
                set y2 [expr $y0]
            .f.c create line [dx 0] [dy 0]  [dx 1] [dy 0]  -fill black -width 1 -arrow last -arrowshape {10 15 5}
                #Y-achse
                set x1 [expr $x0]
                set y1 [expr $y0+$h]
                set x2 [expr $x0]
                set y2 [expr $y0-$h]
            .f.c create line $x1 $y1 $x2 $y2 -fill black -width 1 -arrow last -arrowshape {10 15 5}


            set GB(id_kurve) [.f.c create line [dx 0] [dy 1] [dx 0] [dy 1] -width 2 -fill blue]
    }


####################################
    proc view_titel {} {
            global GB
            .f.c create text 10 20 -text "Angular frequency  \t= [format %.5f $GB(omg)]" -anchor nw
            .f.c create text 10 40 -text "Eigenfrequency \t= [format %.5f $GB(frq)]" -anchor nw
            .f.c create text 10 60 -text "Period       \t= [format %.5f $GB(prd)]" -anchor nw
            .f.c create text 10 80 -text "crit. Dampfung\t= [format %.5f $GB(ckr)]" -anchor nw
    }

#start
        view_init

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Have Fun!