Vertical Spring Model  

This basic model of a vertical spring can be related to a variety of other models including the LRC Circuit model.

THE MODEL
Vensim Version STELLA Version

[Diagram Level | Equations Level | Graphs ]



Height(t) = Height(t - dt) + (Change_in_height) * dt
INIT Height = 1.5+Weight/Spring_K
Change_in_height = Change_in_Position
Gravitational_PE = 9.8*Mass*Height
Kinetic_Energy = .5*Mass*(Velocity)^2
Spring_PE = .5*Spring_K*(Position)^2
Total_Energy = Gravitational_PE+Kinetic_Energy+Spring_PE
Position(t) = Position(t - dt) + (Change_in_Position) * dt
INIT Position = -1.5+Weight/Spring_K
Change_in_Position = Velocity
Velocity(t) = Velocity(t - dt) + (Acceleration) * dt
INIT Velocity = 0
Acceleration = Net_Force/Mass
Mass = 2
Net_Force = Restoring_Force+Weight
Period = 2*PI*SQRT(Mass/Spring_K)
Restoring_Force = -Spring_K*Position
Spring_K = 35
Weight = -9.8*Mass
Time Specs
Range: 0-4, dT = 0.0125, Integration Method = Runge-Kutta 4



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