PENYELESAIAN SECARA EKSAK ANALISA OSILATOR HARMONIK TERENDAM METODE 1/2 INTERVAL




m=1.2x103
k=1.25x106
b=1.4x102;
g=9.8
yo=pertambahan panjang mula mula pegas = 1
t1=Masukkan akar waktu (t1) pertama    = 1
t2=Masukkan akar waktu (t2) kedua      = 2
Fo=gaya mula mula                      = 50
M =Masukkan jumlah iterasi              = 12
wo=sqrt(k/m)
wo=sqrt(1.25x106/1.2x103)
wo=32.2749
w =sqrt((wo)^2-(b^2)/(2*((m)^2)))
w =sqrt((32.27-(1.4x102)^2/(2*(1.2x103)))
w =32.2748

1.       Menghitung pada interval awal, t1=1 dan t2=2 sehingga diperoleh
      f1=                 Yt1
      f2=                 Yt2
      f1=                 (yo*cos(wo*t1))+(yo*sin(wo*t1))+((Fo/(wo^2-w^2))*(cos(w*t1)))+ ((m*g)/(wo^2))
f1=                       (1*cos(32.2749*1))+(1*sin(32.2749*1))+((50/32.2749^2-32.278))* cos(32.2748*1)))+(( 1.2x103*9.8)/( 32.2749^2))
   = 4.8126x103
F2=                      (yo*cos(wo*t2))+(yo*sin(wo*t2))+((Fo/(wo^2-w^2))*(cos(w*t2)))+ ((m*g)/(wo^2))

f2=                       (1*cos(32.2749*2))+(1*sin(32.2749*2))+((50/32.2749^2-32.278))* cos(32.2748*2)))+(( 1.2x103*9.8)/( 32.2749^2))
   = -1.0630x103
2.       Menghitung estimasi sub interval pertama;

t3= (t1+t2)/2
   = (1+2)/2
   = 1.5
ft1=(1*cos(32.2749*1.5))+(1*sin(32.2749*1.5))+((50/32.2749^2-32.278))* cos(32.2748*1.5)))+(( 1.2x103*9.8)/( 32.2749^2))
  =  -2.0383x103
3.       Menghitung interval t4 dari t3 dan t2;
ft2=Y(t)                     
t4= (t3+t2)/2
   = (1.5+2)/2
   = 1.75
ft2=(1*cos(32.2749*1.75))+(1*sin(32.2749*1.75))+((50/32.2749^2-32.278))* cos(32.2748*1.75)))+(( 1.2x103*9.8)/( 32.2749^2))
  =  7.3310x103

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