You can try using the structure shown in the attached model.

Sample.msim

This one uses MapleSim Multibody visualization components to get a shape for 3d visualization. The motion is obtained by a dedicated motion driver, which enforces a trapezoidal motion profile. However, you can also replace that with an applied force component if you require.

If you need to go for better (more accurate) 3d visualization, you need to have the 3D model. At this point, you have two options. 

1. Use MapleSim's CAD toolbox to automatically detect the different parts of the 3D file and import them into MapleSim with a click of a button while preserving the dimensions and assembly offsets of the parts from the original 3D assembly.

2. Manually export the different parts as component files and manually import them into MapleSim using the CAD visualization component, while making sure the dimensions are entered exactly as they were in the model. In this method, the dimensions (spaces, offsets etc.) of different 3d Parts must be implemented using MapleSim components (e.g., rigid arm) and their dimensions must be manually entered to be identical to those in the 3d model. 

Hope this helps, let me know.

One possible way could be to use a prismatic joint with spring and damper as shown in the figure below

The planer joint makes sure that the bottom point can move around in the horizontal plane. The applied force makes the compliance move up and down. The small masses make sure that we don't apply non zero forces to zero mass points. 

Model attached.MultibodySpring.msim

Hi,

Q: Is it possible to edit 3D work space directly in maplesim? How?

A: Yes it is certainly possible to manipulate 3D objects (initial locations mainly) in the 3D workspace in MapleSim. However, we would definitely recommend not doing such adjustments. Any adjustments made in the 3D workspace will be updated in the model canvas (initial positions etc). It is much more advisable to make all your changes from the model canvas and through the model parameters. 

Q: Can we add a static (fixed) cylinder around a piston (translating cylinder) in the 3D workspace?

A: Yes, but again don't do it through the 3D workspace. The attached model does this using visualization components and motion drivers. The cylinder visualization component has inside radius options.

Use: Piston.msim

Q: Can we draw in maple drawing and add it to maplesim 3D space?

A: Absolutely. Maple can create STL files through the exportplot command inside plottools package. Once you have an STL file available to you, you can attach it to any maplesim model by using the CAD visualization component found inside > Multibody > Visualization  > CAD Geometry.

https://www.maplesoft.com/support/help/Maple/view.aspx?path=Formats/STL

To impose constraints into revolute joint, one method could be to use a elasto-backlash component on top of a revolute joint as shown in the figure below.

The attached model implements the double pendulum with the second revolute joint with the elasto backlash component. The parameter 'b' in the elasto backlash component determines what is the range of rotation where there would be no resistance from the joint (free motion). The component is hardcoded to assume that the range is symmetric around 0 (mean location). so rotation = -b/2 rad to b/2 rad. 

DoublePendulum.msim

Model is attached for reference. Hope this helps.

I understand this might not be feasible for you but will it be possible for you to do a Search and Replace to change all single underscore to double underscore? I did it with Maple worksheet and it worked. I even changed one of the entries to the 2D math format.. and it worked too

As you can see here, I have solved for alpha, but not in closed form, but using an fsolve command (to solve it numerically). This is because the equation you have (If I have understood it correctly... Please confirm if I have messed up), is transcendental in nature and symbolically solving them can be impossible at times.

Also, the equation has multiple solutions.. take a look at the plot. Worksheet attached herewith, Hope it helps

EquationsSolve.mw

If you want to create a matrix variable, I would use the "Matrix" command. 

The SignalProcessing package provides commands for manipulating signals. Specifically, these commands work on samples of signals stored in Vectors with datatype float[8] or complex[8].

You will find a complete list of the commands available by typing ?SignalProcessing in Maple.

As an example, I have modified your worksheet to evaluate the DFT of the solution of the ODE you were looking at.I hope this would help you in some way. Feel free to ask for clarifications.

The figure below shows the output of the attached worksheet for the signal u1(t)

ODEs_withDFT.mw

This thesis uses Groebner basis extensively. I think you will find your answer in chapter 3

https://uwspace.uwaterloo.ca/bitstream/handle/10012/5844/Uchida_Thomas.pdf;sequence=1

Q: What do you mean by creating a worksheet? how can we do that in maple?

A Maple worksheet is a standard file in Maple. It looks like this

You can open a new Maple worksheet by clicking on File > New > Worksheet mode.

In the example shown above, you can see the equation you provided and the parameter values you specified later. They are substituted in the equation so that we deal with two variables only.

As for your particular equation, I have tried to find the maximum value of R by using Maple's Optimization ToolBox. 

Please take a look at the figure below to see if this helps. I have used the implicitplot command to create a plot of the function, and then I have used the GlobalSolve command to find the maximum of R. For the optimization I have specified R as the objective function and the equation as the constraint.

Let me know if this helps.