第7章 複合運動

７．１　多重振り子

【リスト7-1】二重振り子
from tkinter import *
from tkinter import messagebox
import random, math, time
def array(N1, N2=0, N3=0):
    if N2 == 0 and N3==0: return [0 for i in range(N1)]
    elif N3 == 0: return [[0 for i in range(N2)] for j in range(N1)]
    else: return [[[0 for i in range(N3)] for j in range(N2)]
                  for k in range(N1)]
def Sim(root):#■シミュレーション
    global t, dt, ID1, ID2, aTH, bTH, aVel, bVel,adTH, bdTH
    global PaG, PbG, LBL,aAcc, bAcc, aX, aY, bX,bY
    t += dt; root.title("time = %9.6f" % t)
    CosDTh=math.cos(aTH[ID2] - bTH[ID2])
    SinDTh=math.sin(aTH[ID2] - bTH[ID2])
    SinATh=math.sin(aTH[ID2]) ; SinBTh=math.sin(bTH[ID2])
    aAlf2 =aVel[ID2]*aVel[ID2]; bAlf2 =bVel[ID2]*bVel[ID2]
    #おもり a の計算
    aAcc[ID1]=(dt*(myuC*SinDTh*(LbL*bAlf2+aAlf2*CosDTh) +
                   PaG *SinATh - myuC*PbG*SinBTh*CosDTh) /
               (myuC*(CosDTh*CosDTh) - 1))
    aVel[ID1]=(aVel[ID2]+aAcc[ID1])*(1-Myu)    # 速度計算
    adTH[ID1]= aVel[ID1]*dt; aTH[ID1] = aTH[ID2]+adTH[ID1]
    aX[ID1] = PaL*math.sin(aTH[ID1])           # 位置計算
    aY[ID1] = PaL*math.cos(aTH[ID1])
    #おもり b の計算
    bAcc[ID1]=(dt*(aAlf2*SinDTh-aAcc[ID2]/dt*CosDTh -
                   PbG*SinBTh)/LbL)
    bVel[ID1]=(bVel[ID2]+bAcc[ID1])*(1-Myu)     #速度計算
    bdTH[ID1]= bVel[ID1]*dt; bTH[ID1]= bTH[ID2]+ bdTH[ID1]
    bX[ID1]= aX[ID1] + PbL*math.sin(bTH[ID1])   # 位置計算
    bY[ID1]= aY[ID1] + PbL*math.cos(bTH[ID1])
def draw(canvas, ID1):#■おもり位置の変更
    global XStart, YStart, SC, aX, bX, aY, bY
    global L1ID, L2ID, B2ID, B3ID
    X1 = XStart; Y1 = YStart
    X2 = aX[ID1]*SC + XStart; Y2 = aY[ID1]*SC + YStart
    X3 = bX[ID1]*SC + XStart; Y3 = bY[ID1]*SC + YStart
    canvas.coords(L1ID, X1, Y1, X2, Y2)
    canvas.coords(L2ID, X2, Y2, X3, Y3)
    canvas.coords(B2ID, X2-4, Y2-4, X2+4, Y2+4)    
    canvas.coords(B3ID, X3-4, Y3-4, X3+4, Y3+4)
#    軌跡を表示するときは，上1行をコメントにし以下の5行のコメントを外す
#    BXY=canvas.coords(B3ID)
#    XX=(BXY[0]+BXY[2])/2;YY=(BXY[1]+BXY[3])/2;
#    canvas.coords(B3ID, XX, YY, XX, YY)
#    canvas.itemconfig(B3ID, fill="green", outline="")
#    B3ID=canvas.create_oval(X3-4, Y3-4, X3+4, Y3+4, fill="red")
#メイン処理    
root=Tk(); root.title("二重振り子")
canvas=Canvas(root, width=240,height=250, bg="white");canvas.pack()
#パラメータ設定
PI  = math.pi; SC = 2000; XStart = 120; YStart = 10
PaL =0.05; PbL = 0.05             # 棒の長さ
PaM =0.02; PbM = 0.02             # おもりの重さ
g   =9.8                          # 重力加速度
dt  =0.005                        # 時間刻み
Myu =0.001                        # 粘性抵抗(人工拡散項を考慮する)
LOOP=20000                        # シミュレーション回数
# 事前計算
myuC=PbM/(PaM+PbM)
PaG=g/PaL; PbG=g/PbL; LbL=PbL/PaL
#初期設定(接頭文字a, bがおもりを示す)     
aTH=array(2); bTH=array(2)         # θ
aTH[1]=30*PI/180; bTH[1]=10*PI/180
adTH  =array(2); bdTH  =array(2)   # Δθ
aAcc=array(2); bAcc=array(2)       # 加速度
aVel =array(2); bVel =array(2)     # 速度  
aX=array(2); aY=array(2)           # a の XY 座標
bX=array(2); bY=array(2)           # b の XY 座標
aX[1] = PaL * math.sin(aTH[1])
aY[1] = PaL * math.cos(aTH[1])
bX[1] = aX[1] + PbL * math.sin(bTH[1])
bY[1] = aY[1] + PbL * math.cos(bTH[1])
t = 0; ID1 = 0; ID2 = 1
#初期描画
X1 = XStart; Y1 = YStart
X2 = aX[1]*SC + XStart; Y2 = aY[1]*SC + YStart
X3 = bX[1]*SC + XStart; Y3 = bY[1]*SC + YStart
L1ID=canvas.create_line(X1, Y1, X2, Y2, fill="blue", width=2)
L2ID=canvas.create_line(X2, Y2, X3, Y3, fill="blue", width=2)
B1ID=canvas.create_oval(X1-2, Y1-2, X1+2, Y1+2, fill="#FF7700")
B2ID=canvas.create_oval(X2-4, Y2-4, X2+4, Y2+4, fill="red")
B3ID=canvas.create_oval(X3-4, Y3-4, X3+4, Y3+4, fill="red")
root.update()
#シミュレーション開始
for k in range(LOOP):
    time.sleep(0.01)
    Sim(root); draw(canvas, ID1); root.update()
    ID = ID1; ID1 = ID2; ID2 = ID

【リスト7-2】多重振り子
from tkinter import *
from tkinter import messagebox
import random, math, time
def array(N1, N2=0, N3=0):
    if N2 == 0 and N3==0: return [0 for i in range(N1)]
    elif N3 == 0: return [[0 for i in range(N2)] for j in range(N1)]
    else: return [[[0 for i in range(N3)] for j in range(N2)]
                  for k in range(N1)]
def Sim(root):#■シミュレーション
    global t, dt, g, KFact,PaM, F, ID1, ID2, KFact, aTH, adTH
    t += dt; root.title("time = %9.6f" % t)
    mG0 = 0; DMg = PaM * g
    for i in range(Num):
        mG0 += DMg; F[i]= -mG0 * math.sin(aTH[i][ID1])
        adTH[i][ID2]= adTH[i][ID1]+ F[i]*dt; mG0 *=KFact
    TH = 0
    for i in range(Num-1, -1, -1):
        TH += adTH[i][ID1]
        adTH[i][ID2]= adTH[i][ID2]* (1 - Myu)
        aTH[i][ID2]= aTH[i][ID1]+ adTH[i][ID2]*dt
def draw(canvas, ID1):#■おもり位置の変更
    global XStart, YStart, SC, aX, bX, aY, bY,PaL
    global LID,BID
    X1 = XStart; Y1 = YStart
    for i in range(Num-1,-1, -1):
        cosTH = math.cos(aTH[i][ID1]); sinTH = math.sin(aTH[i][ID1])
        X2 = PaL * sinTH + X1;   Y2 = PaL * cosTH + Y1
        canvas.coords(LID[i], X1, Y1, X2, Y2)
        canvas.coords(BID[i], X2-2, Y2-2, X2+2, Y2+2)
        X1 = X2; Y1 = Y2
#メイン処理    
root=Tk(); root.title("二重振り子")
canvas=Canvas(root, width=400,height=500, bg="white");canvas.pack()
#パラメータ設定
PI  = math.pi; SC = 2000; XStart = 200; YStart = 10
PaL =5             # 棒の長さ
PaM =0.1           # おもりの重さ
Num=50             # 分割数
TH=30*PI/180       # 初期角度
g   =9.8           # 重力加速度
dt  =0.05          # 時間刻み
Myu =0.001         # 粘性抵抗(人工拡散項を考慮する)
KFact=1            #伝達係数
LOOP=2000           # シミュレーション回数
#初期設定(接頭文字a, bがおもりを示す)     
a=array(Num,2);F=array(Num);LID=array(Num); BID=array(Num)
aTH=array(Num,2); adTH=array(Num,2)  # θ, Δθ
for i in range(Num):
    aTH[i][0]=TH; adTH[i][0]=0
t=0; ID1=0;ID2=1
#初期描画
X1 = XStart; Y1 = YStart
canvas.create_oval(X1-2, Y1-2, X1+2, Y1+2, fill="yellow")
for i in range(Num-1,-1, -1):
    cosTH = math.cos(aTH[i][ID1]); sinTH = math.sin(aTH[i][ID1])
    X2 = PaL * sinTH + X1;   Y2 = PaL * cosTH + Y1
    LID[i]=canvas.create_line(X1, Y1, X2, Y2, fill="blue", width=1)
    BID[i]=canvas.create_oval(X2-2, Y2-2, X2+2, Y2+2, fill="red")
    X1 = X2; Y1 = Y2
root.update()
#シミュレーション開始
for k in range(LOOP):
    time.sleep(0.1); Sim(root); draw(canvas, ID1); root.update()
    ID = ID1; ID1 = ID2; ID2 = ID


７．２　おもりとバネ

【リスト7-3】おもりをゴム紐で引っ張る動き
from tkinter import *
import time
root=Tk();root.title("おもりをゴム紐で引っ張る動き")
canvas=Canvas(root,width=500,height=500, bg="white");canvas.pack()
canvas.focus_set()
Kfact=0.05; Rfact=0.5; mouseX=100; mouseY=100
PX = 100; PY = 100; VX = 0; VY = 0
LID=canvas.create_line(mouseX, mouseY, PX, PY, fill="blue",width=2)
BID=canvas.create_oval(PX-5,PY-5,PX+5,PY+5,fill="red")
#■計算
def calc(canvas):
    global Kfact, Rfact, PX, PY, VX, VY, mouseX, mouseY, LID, BID
    VX = (VX - Kfact*(PX - mouseX))*Rfact
    VY = (VY - Kfact*(PY - mouseY))*Rfact
    PX += VX; PY += VY
    canvas.coords(LID,mouseX, mouseY, PX, PY)
    canvas.coords(BID,PX-5,PY-5,PX+5,PY+5)
#■マウス移動
def MouseMotion(event):
    global mouseX, mouseY
    mouseX=event.x; mouseY= event.y
#図形上でのクリックイベント   
def deleteLine(event):
    canvas.delete('current')
    print("Line select Button No.",event.num)
#■バインドの指定
canvas.bind("<Motion>", MouseMotion)
#■メインループ
while True: root.update();time.sleep(0.01); calc(canvas)

【リスト7-4】　棒でつながった球の運動
from tkinter import *
import time,math,winsound
root=Tk();root.title("棒でつながった球")
canvas=Canvas(root,width=500,height=270, bg="white");canvas.pack()
canvas.focus_set()
P1M = 1500; P2M = 200; SLen=100;
Myu = 0.02; Kfact = 10; G=0.98; TimerInt = 0.01
Y1 =10; X1 =200; X2 = X1 + SLen; Y2 = 30
V1X= 0; V1Y= 0; V2X= 0; V2Y=0;
canvas.create_rectangle(0,250,510,280, fill="#775522",outline="")
canvas.create_line(0,250,510,250, fill="black",width=2)
LID=canvas.create_line(X1,Y1, X2, Y2, fill="blue",width=2)
B1ID=canvas.create_oval(X1-6,Y1-6,X1+6,Y1+6,fill="red")
B2ID=canvas.create_oval(X2-3,Y2-3,X2+3,Y2+3,fill="yellow")
#■計算
def calc(canvas):
    global Kfact, P1M, P2M, SLen, X1, Y1, X2, Y2
    global V1X, V1Y,V2X, V2Y, mouseX, mouseY, LID, B1ID,B2ID
    Mu1=1-Myu; DX = X1 - X2; DY = Y1 - Y2
    DL = math.sqrt(DX*DX + DY*DY); HX = DX/DL; HY = DY/DL
    FL = -Kfact*(DL - SLen); FX = HX*FL; FY = HY*FL
    A1X =  FX*0.5/P1M; A1Y =  FY*0.5/P1M
    A2X = -FX*0.5/P2M; A2Y = -FY*0.5/P2M
    V1X = (A1X + V1X)*Mu1; V1Y = (A1Y + V1Y + G)*Mu1
    V2X = (A2X + V2X)*Mu1; V2Y = (A2Y + V2Y + G)*Mu1
    X1 = X1 + V1X; Y1 = Y1 + V1Y
    X2 = X2 + V2X; Y2 = Y2 + V2Y
    if Y1>(250-6):
        if V1Y>1: winsound.Beep(523,100)
        Y1 = (250-6); V1Y = -V1Y
    if Y2>(250-3):
        if V2Y>1: winsound.Beep(1026,50)    
        Y2 = (250-3); V2Y = -V2Y
    canvas.coords(LID,X1,Y1,X2,Y2)
    canvas.coords(B1ID,X1-6,Y1-6,X1+6,Y1+6)
    canvas.coords(B2ID,X2-3,Y2-3,X2+3,Y2+3)
#■左ボタンダウン
def leftMouseDown(event):#ダウン
    global X1, Y1; X1 = event.x; Y1 = event.y
#■バインドの指定
canvas.bind("<Button-1>",leftMouseDown)
#■メインループ
while True: root.update();time.sleep(TimerInt); calc(canvas)


７．３　連続バネ/ゴム紐の運動

【リスト7-5】連続バネ
from tkinter import *
import time,math
def array(N1, N2=0, N3=0):
    if N2 == 0 and N3==0: return [0 for i in range(N1)]
    elif N3 == 0: return [[0 for i in range(N2)] for j in range(N1)]
    else: return [[[0 for i in range(N3)] for j in range(N2)]
                  for k in range(N1)]
#パラメータ設定
NumNode=30     #要素数(節点数-1)
Mass=5         #節点質量
LenNode=5      #節点間の長さ
Myu=0.002      #粘性抵抗
Kfact=5        #節点間のバネ係数
Gravity=0.98   #重力
DT=0.001       #時間刻み
TimerInt=0.001 #スリープ時間
MX=NumNode+1   #節点数(要素数+1: 配列サイズ)
sCapture=False    #画面キャプチャモード
X=array(MX);Y=array(MX);XB=array(MX);YB=array(MX);
VX=array(MX);VY=array(MX);LID=array(NumNode)
def initP():#■座標値等の初期設定
    global MX,X,Y,XB,YB, VX, VY
    for i in range(MX):
        X[i]=20+i*LenNode*1.5; Y[i]=40
        XB[i]=X[i];YB[i]=Y[i]; VX[i]=-200; VY[i]=100
def force(X1, Y1, X2, Y2):#■節点間の力の計算
    global LenNode, Kfact
    dx = X2-X1; dy = Y2-Y1; R=[0,0]
    DR = math.sqrt(dx * dx + dy * dy)
    if DR < LenNode  : DR = LenNode
    LL = ((DR-LenNode)*Kfact) / DR
    R[0]= LL * dx; R[1]= LL * dy
    return R
def calc(canvas):#■計算
    global NumNode,Kfact, Rfact, X, XB, Y,YB, VX, VY, DT, Mass,Myu, Gravity
    for i in range(NumNode+1): # 壁面・床の処理
        if Y[i] > 260: Y[i]= 260; VY[i]= -abs(VY[i])
        if Y[i] <  10: Y[i]=  10; VY[i]= abs(VY[i])
        if X[i] > 260: X[i]= 260; VX[i]= -abs(VX[i])
        if X[i] <  10: X[i]=  10; VX[i]= abs(VX[i])
    for i in range(NumNode+1): # 力の計算・加速度
        X[i] = XB[i] + VX[i]*DT
        Y[i] = YB[i] + VY[i]*DT
        if   i == 0: F =force(X[i],Y[i], X[i+1], Y[i+1])
        elif i == NumNode: F =force(X[i],Y[i], X[i-1], Y[i-1])
        else:
            F1 = force(X[i],Y[i], X[i+1], Y[i+1])
            F2 = force(X[i],Y[i], X[i-1], Y[i-1])
            F[0]=F1[0]+F2[0]; F[1]=F1[1]+F2[1]
        VX[i]= (VX[i] + F[0]/Mass)*(1 - Myu)
        VY[i]= (VY[i] + F[1]/Mass + Gravity)*(1 - Myu)
    for i in range(NumNode+1): XB[i]=X[i]; YB[i]=Y[i]
    for i in range(NumNode):
        canvas.coords(LID[i], X[i], Y[i],X[i+1],Y[i+1])
def leftMouseDown(event):#■左ボタンクリック
    global mouseX, mouseY, XB, YB, LenNode, Kfact, sCapture
    if sCapture:#画面キャプチャ用処理
        for i in range(20):
            calc(canvas);root.update()
        return
    mouseX=event.x; mouseY= event.y
    for k in range(30):#引っ張りあげたときの形状確定のための繰返し
        XB[0]=mouseX; YB[0]=mouseY
        for i in range(NumNode):
            t = i + 1
            dx = XB[t]-XB[i]; dy = YB[t] - YB[i]
            DR = math.sqrt(dx * dx + dy * dy)
            if DR < LenNode  : DR = LenNode
            FF = ((DR-LenNode)+Kfact)*0.5 / DR
            XB[i] = XB[i] + dx * FF
            XB[t] = XB[t] - dx * FF
            YB[i] = YB[i] + dy * FF
            YB[t] = YB[t] - dy * FF
    calc(canvas)
    sCapture=True
def rightMouseDown(event):#■右ボタンクリック
    global sCapture;
    if sCapture: sCapture=False
    else: initP()
#■メイン処理
root=Tk();root.title("連続バネ／ゴム紐の運動")
canvas=Canvas(root,width=270,height=270, bg="white");canvas.pack()
canvas.focus_set(); initP(); mouseX=0; mouseY=0
canvas.create_rectangle(8,8,262,262, fill="", outline="blue",width=2)
for i in range(NumNode):#初期形状表示
    LID[i]=canvas.create_line(X[i], Y[i],X[i+1],Y[i+1],fill="red",width=2)
canvas.bind("<Button-1>",leftMouseDown)#■バインドの指定
canvas.bind("<Button-3>",rightMouseDown)
#■メインループ
while True:
    time.sleep(0.01);root.update();
    if not sCapture: calc(canvas)

７．４　ふたつの振り子

【リスト7-6】 2つの振り子のおもりの衝突
from tkinter import *
import time,math,winsound
def array(N1, N2=0, N3=0):
    if N2 == 0 and N3==0: return [0 for i in range(N1)]
    elif N3 == 0: return [[0 for i in range(N2)] for j in range(N1)]
    else: return [[[0 for i in range(N3)] for j in range(N2)]
                  for k in range(N1)]
PI=math.pi; PI3=PI/3
Myu = 0.0           # 粘性抵抗
e   = 1             # 衝突係数
DT=0.01             # 時間刻み
M1=10; M2=10        # 振り子のおもりの重さ
R1=10; R2=10        # 振り子のおもり半径
L=100               # 振り子の棒の長さ
X0=120; Y0=10       # 振り子を吊るす位置の中心位置
X1=X0-R1; X2=X0+R2  # 振り子を吊るす位置のX座標
RID=array(2,2);TH=array(2);V=array(2)# 配列宣言
TH[1]=PI3           # 振り子 2 のおもりの初期位置
#■メイン処理
root=Tk();root.title("ふたつの振り子")
canvas=Canvas(root,width=240,height=150, bg="white");canvas.pack()
canvas.focus_set()
def initPend(canvas, X0, Y0, L, R, TH, C):#■振り子初期位置の描画
    RT=[0,0]; X2=X0+L*math.sin(TH); Y2=Y0+L*math.cos(TH)
    RT[0]=canvas.create_line(X0,Y0, X2, Y2, fill="black",width=2)
    canvas.create_oval(X0-2,Y0-2,X0+2,Y0+2,fill="yellow")
    RT[1]=canvas.create_oval(X2-R,Y2-R,X2+R,Y2+R,fill=C)
    return RT
RID[0]=initPend(canvas, X1,Y0, L,R1,TH[0],"red")
RID[1]=initPend(canvas, X2,Y0, L,R2,TH[1],"blue")
def movePend(canvas, RT, X0, Y0, L, R, TH):#■振り子位置移動
    X2=X0+L*math.sin(TH); Y2=Y0+L*math.cos(TH)
    canvas.coords(RT[0], X0,Y0, X2, Y2)
    canvas.coords(RT[1],X2-R,Y2-R,X2+R,Y2+R)
def checkCollision():#■おもり衝突のチェック
    global X1,X2, Y0, R1, R2; RR=R1+R2;RR=RR*RR
    XX1=X1+L*math.sin(TH[0]); YY1=Y0+L*math.cos(TH[0])
    XX2=X2+L*math.sin(TH[1]); YY2=Y0+L*math.cos(TH[1])
    DX=XX1-XX2; DY=YY2-YY1
    if DX*DX+DY*DY<=RR: return True
    return False
def Collision():#■おもり衝突時の速度変更
    global e, M1, M2; MM=M1+M2; ee=1+e ; VV=V[0]
#    if abs(V[0]-V[1])>0.05: winsound.Beep(1026,50)
    V[0]+= M2*ee*(V[1]-VV)/MM
    V[1]-= M1*ee*(V[1]-VV)/MM
def calc():#■衝突以外のおもりの移動の計算
    global V,TH,DT,Myu
    for i in range(2):
        V[i]-=DT*(math.sin(TH[i])+V[i]*Myu)
        TH[i]+=DT*V[i]
def dsp(canvas):#■振り子の描画
    global RID,X1,X2, Y0,L,R1,R2,TH
    movePend(canvas,RID[0], X1,Y0, L,R1,TH[0])
    movePend(canvas,RID[1], X2,Y0, L,R2,TH[1])
#■メインループ
while True:
    calc(); dsp(canvas);root.update()
    if checkCollision():Collision()
    time.sleep(0.0001)
   

７．５　強制振動と振動の伝達

【リスト7-7】強制振動と振動の伝達
from tkinter import *
import time,math,winsound
def array(N1, N2=0, N3=0):
    if N2 == 0 and N3==0: return [0 for i in range(N1)]
    elif N3 == 0: return [[0 for i in range(N2)] for j in range(N1)]
    else: return [[[0 for i in range(N3)] for j in range(N2)]
                  for k in range(N1)]
PI=math.pi
V1=0; X1=100; L1= 50; H1=50; M1=1.0; Myu1=0.02 # 物体 1 データ
V2=0; X2=300; L2=100; H2=50; M2=1.5; Myu2=0.02 # 物体 2 データ
DT=0.01; DTH=PI*DT; Kfact=1                    # 実行用パラメータ
Hist=array(400,2); IHist=0; iDsp=10            # 履歴表示用
def history(canvas):#■履歴表示
    global Hist,IHist, X1, X2
    Hist[IHist][0]=X1-100; Hist[IHist][1]=X2-300;IHist+=1
    if IHist>=400: IHist=0
    canvas.delete("Graph"); GH=200; GH1=GH-30; GH2=GH+30
    ip=IHist;GX1=Hist[ip][0]+GH; GX2=Hist[ip][1]+GH
    canvas.create_line(50,GH, 450, GH, fill="green",tag="Graph")
    for i in range(399):
        ip+=1
        if ip>=400: ip=0
        GN1=Hist[ip][0]+GH; GN2=Hist[ip][1]+GH
        if ip % 100==0:
            canvas.create_line(i+50,GH1, i+50, GH2, fill="green",tag="Graph")
        canvas.create_line(i+50,GX1, i+51, GN1, fill="red",tag="Graph")
        canvas.create_line(i+50,GX2, i+51, GN2, fill="blue",tag="Graph")
        GX1=GN1; GX2=GN2
def calc(F):#■計算                         
    global M1,M2, Myu1,Myu2,X1,V1,X2,V2,Kfact
    FS=(X2-X1-200)*Kfact
    Acc=(F+FS)/M1; V1=(V1+Acc*DT)*(1-Myu1); X1+=V1*DT
    Acc=-FS/M1; V2=(V2+Acc*DT)*(1-Myu2); X2+=V2*DT
def initDraw(canvas,X,L,H,C):#■物体初期表示
    LL=L/2;
    return canvas.create_rectangle(X-LL,100, X+LL, 100-H,
                                   fill=C,width=2)
def initLine(canvas,X1, X2,H,C):#■バネを直線で描く
    HH=100-H/2;
    return canvas.create_line(X1,HH, X2, HH, fill=C,width=2)
def Draw(canvas,ID, X,L,H):#■物体の表示(座標位置変更)
    LL=L/2; canvas.coords(ID, X-LL,100, X+LL, 100-H)
def DrawLine(canvas,ID, X1, X2, H): #■バネの表示(座標位置変更)
    HH=100-H/2; canvas.coords(ID, X1,HH, X2, HH)
root=Tk();root.title("強制振動")
canvas=Canvas(root,width=480,height=400, bg="white");canvas.pack()
LID= initLine(canvas,X1,X2,H1,"black")
ID1 = initDraw(canvas, X1, L1, H1,"red")
ID2 = initDraw(canvas, X2, L2, H2,"blue")
TH=0;N=0
while True:
    root.update(); time.sleep(0.001)
    calc(200*math.sin(TH)); TH+=DTH
    DrawLine(canvas,LID, X1, X2, H1)
    Draw(canvas, ID1, X1, L1, H1)
    Draw(canvas, ID2, X2, L2, H2)
    N+=1
    if N % iDsp==0: history(canvas)