Vertical 2 mass 2 spring problem - IVP

1. The problem statement, all variables and given/known data

mass1 = 10kg connected to ceiling by a spring
mass2 = 2kg connected to mass1 by a spring

2m/s is applied to mass 1 in the downward direction (positive direction) to get the system in motion
At equilibrium Mass 1 is 2m from the ceiling while mass 2 is 4m from the ceiling

10 x1’’ = -100x1 + 120(x2-x1)
2 x2’’ = -120(x2-x1)

find solution over time period 0<=t<=10sec

Need to use Eulers method

2. Relevant equations



3. The attempt at a solution

Reduce equations to:
x1’’ = 12x2-22x1
x2’’ = 60x1 – 60x2


Let:
x1’ = z
x1’’ = dz/dx
z(0) = 2 m/s ????


Let:
x2’ = v
x2’’ = dv/dt
v(0) = 0 m/s ?????


dx1/dx = z = f1(x1,x2,z)
dz/dx = 12x2-22x1 = f2(x1,x2,z)
dx2/dx = v = f3(x1,x2,v)
dv/dx = 60x1 - 60x2 = f4(x1,x2,v)



Not sure if I have these initial conditions set up properly??
Please help, Thanks
 
Last edited:

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