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(testmodels-cartesianspringdampertest)=
# CartesianSpringDamperTest.py

You can view and download this file on Github: [CartesianSpringDamperTest.py](https://github.com/jgerstmayr/EXUDYN/tree/master/python/TestModels/CartesianSpringDamperTest.py)

```{code-block} python
:linenos:

#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
# This is an EXUDYN example
#
# Details:  A mass point held by a `CartesianSpringDamper` against a constant force, integrated over
#           1 s in 1000 steps: the x-displacement at the end, which agrees with the analytical
#           solution to about 3e-6.
#           The model compares against a reference value written into it, so its
#           result is that difference and its reference solution is 0 (#2632).
#
# Author:   Johannes Gerstmayr
# Date:     2019-11-01, reworked 2026-09-24
#
# Copyright:This file is part of Exudyn. Exudyn is free software. You can redistribute it and/or modify it under the terms of the Exudyn license. See 'LICENSE.txt' for more details.
#
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

import exudyn as exu
from exudyn.utilities import * #includes itemInterface and rigidBodyUtilities
import exudyn.graphics as graphics

testIsActive = exu.sys.get('testIsActive', False)
exu.sys['testTolerance'] = 4e-13 #the tolerance RunAllModelUnitTests used for these ten

SC = exu.SystemContainer()
mbs = SC.AddSystem()

L=0.5
mass = 1.6
k = 4000
omega0 = 50 # sqrt(4000/1.6)
dRel = 0.05
d = dRel * 2 * 80 #80=sqrt(1.6*4000)
u0=-0.08
v0=1
f = 80
x0 = f/k

#node for mass point:
n1=mbs.AddNode(Point(referenceCoordinates = [L,0,0], initialCoordinates = [u0,0,0], initialVelocities= [v0,0,0]))

#add mass points and ground object:
objectGround = mbs.AddObject(ObjectGround(referencePosition = [0,0,0]))
massPoint = mbs.AddObject(MassPoint(mass = mass, nodeNumber = n1))

#marker for constraint / springDamper
groundMarker = mbs.AddMarker(MarkerBodyPosition(bodyNumber = objectGround, localPosition= [0, 0, 0]))
bodyMarker = mbs.AddMarker(MarkerBodyPosition(bodyNumber = massPoint, localPosition= [0, 0, 0]))

mbs.AddObject(CartesianSpringDamper(markerNumbers = [groundMarker, bodyMarker], stiffness = [k,k,k], damping = [d,0,0], offset = [L,0,0]))

#add loads:
mbs.AddLoad({'loadType': 'ForceVector',  'markerNumber': bodyMarker,  'loadVector': [f, 0, 0]}) 

#exu.Print(mbs)
mbs.Assemble()

simulationSettings = exu.SimulationSettings()
simulationSettings.solution.file.write=False
tEnd = 1
steps = 1000
simulationSettings.timeIntegration.numberOfSteps = steps
simulationSettings.timeIntegration.endTime = tEnd
simulationSettings.timeIntegration.generalizedAlpha.spectralRadius = 1 #SHOULD work with 0.9 as well
simulationSettings.show.statistics = False

mbs.SolveDynamic(simulationSettings)

u = mbs.GetNodeOutput(n1, exu.OutputVariableType.Position)
uCartesianSpringDamper= u[0] - L
if True:
    errorCartesianSpringDamper = uCartesianSpringDamper - 0.011834933407061654 #until 2022-01-25 (changed jacobians): 0.011834933406052683 #2021-09-27: new JacobianODE2RHS
    #errorCartesianSpringDamper = uCartesianSpringDamper -0.011834933407364412 #2021-02-04: 0.011834933407364412 
else:
    errorCartesianSpringDamper = uCartesianSpringDamper - 0.011834933407594783 #15.12.2019: 0.011834933407594783; beofre 15.12.2019: 0.011834933407038783 #for 1000 steps, endtime=1; accurate up to 3e-6 to exact solution
exu.Print('solution cartesianSpringDamper=',uCartesianSpringDamper)

testResult = abs(errorCartesianSpringDamper)
exu.Print('solution of CartesianSpringDamperTest=', testResult)
exu.sys['testResult'] = testResult
```