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# Double Mass Spring and Damper System

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Definition and Importance

Matlab, short word form for the Matrix Laboratory, is a software system or environment developed by Math Works and consists of a high level programming language that aids in the computations of the numerical date and general visualizations. Matlab as a system consist of five main subsystems which include development environment, the programming language, the matlab library, the application program interface and the graphics.

The development environment consists of various tools put together to aid in the functions and files related to matlab. These tools include the command window, the command history, the editors and debuggers, the browsers and workspace and graphical user interface. The matlab language aids in the developing and creation of programs either the complex applications ones or the quick usable programs that last for shorter periods. The mathematical function library consists of a collection of the algorithms that are used for computation of functions that range from the less complex ones like sines and cosines to more complex ones like the matrix values (Gockenbach 1999).

The graphics enable the representation of all the computation on graphs. It prints the graphs. These graphics are defined and categorized to fit the various levels of the functions for instance the three-dimension and two dimension data visualization and presentation graphics. The graphics also include the other level functions that are relatively low and enable customization of graphics and building of user interface. The matlab application program interface enables writing of other add-ons programs that support matlab. This entails reading of mat-files, developing the routines and using it as a computation engine. It is specifically designed to aid in matrix computations or manipulations, data analysis, plotting of functions graphically, creation of models and a range of applications. This could include communication and processing of the signals, computation of biology and finance, tests and measurements, visual media processing, algorithms applications, and user interface creation (Gockenbach 1999).

Matlab is widely available. This makes the ease to access it more profound. The different downloadable versions of the matlab can be uploaded from the website that is the trial versions which can be converted to a full version through provision of the license key from their online website. Matlab also is compatible and can work with in most of the operating systems of the computers and can be used with other soft wares like java.

This makes it flexible and reliable. Matlab also provides adequate and widely covered documentation that provides information on its usage. This documentation can be in print form or the online format. It contains all the features and how each can be used. The online documentation provides information about the references or sources if the key features of matlab. In addition to all that, matlab is able to influence the memory of a computer by triggering it to process faster when compared to other programs which don’t have a valid connection to the computer memory (Gockenbach 1999).

This matrix computation can be extended to factoring matrices, solving the liners equations using the systems put in place and other programs that have been written in the same programming language. The programming language and tools provide multiple approaches to various orientations enabling a faster solution compared to spreadsheets or other previously used programming languages like java. In an effort to increase efficiency, an additional package is adopted to aid in graphical simulation. This package is known as Simulink.

Simulink

This is a program developed by Math works incorporation to act as a strengthening program to Matlab. It is a model based design that supports simulation, design of various systems level designs, tests and generation of automatic codes and verifies embedded systems. It helps in modeling of dynamic systems and provision of graphical user interface that is used to build block diagrams and analyzing results in addition to effective simulation. Simulink provides flexibility in that the models are arranged hierarchically making it easier to view systems from the higher levels to design levels (Gockenbach 1999).

Simulink Simulation

Since it is integrated with Matlab, simulink enables incorporation of matlab algorithms into models and transfers the results from the simulation process to the matlab for extended analysis. Simulink provides block libraries that can be customized, graphical editors and solvers that model and simulate the changing systems. The add-on product used with matlab helps in parallel computing, test and measurement, generation of codes, biology and finance computation, application deployment, reporting and connecting of database, optimization in mathematics and statistics and processing of signals, prototyping, modeling based on events, graphical simulation and physical modeling (Rouleau 2009).

There are two steps involved in simulation of a dynamic system. The first step involves creation of block diagram using the model graphical editors. This shows the mathematical relationships that are dependent on time among all the inputs and outputs generated by the system. After creating a block program, the simulink software simulates the systems that are represented in a given timeframe to determine their behavior. The user does the commanding and directing of the software. The two systems used include the modeling dynamic system and the simulating dynamic systems. In the modeling dynamic system, simulink software is made up of a library browser that allows selection of the simulink blocks from the libraries composed of different standard blocks (Rouleau 2009).

It is also made up of a graphical editor that helps in drawing the lines that connect to the block. These lines create the model. A simulink block is a diagram or picture model of the system. The diagram comprises of blocks interconnected by lines the out produced by this blocks are either produced continuously or discreetly, that is in specific time zones. The mathematical relationship between the blocks output and the inputs is determined by the type of a block (Rouleau 2009).

The simulating dynamic system involves computing of the systems output and inputs and the state in a given period of time as guided by the information provided by the model of the syste. Running the simulation in the simulink software enables the model compiler to convert the model to a form that can be executed. The compiler determines all the attributes of the signal for instance the name and type of data. It also evaluates the extent of the blocks expressions so as to express their values and simplifying the hierarchy of the blocks and systems in the block (Gockenbach 1999)

Model Designed

The double mass spring damper models are a general representation of the simple suspension systems. The model used in this illustration is the second order system. The discrete model places the physical system to consist of very many rigid bodies that are connected to each other by the springs and the dampers. The dampers are used to enhance resistance to the speed of the physical system. The springs enable the return of the masses to the equilibrium state by restoring the forces that build up. This model uses the simulink blocks to enable the tuning of the system in order to meet the requirements of a typical suspension. These simulink blocks include the damper gain block that is characterized by a constant, mass gain block which is characterized or limited to the total mass suspended, where the total mass is the addition of the nominal mass and variable load mass. The total mass suspended is the parameter of the mass gain block (Rouleau 2009).

Other simulink blocks include the spring gain block whose parameter is the constant of the spring denoted as k, two integrator blocks that are used in the computation of the mass velocity and position. The last simulink block is the band limited disturbance force block that mainly applies the force to the mass. The objective is to use the model to create or develop the double mass spring damper. There is a major problem that is faced while making this design, that is, the bandwidth maybe too high. This is evident from the position signal that happens to be sharp and pointed. The most likely solution to such a problem is tuning the damper and spring values in order to ensure that the system bandwidth does not exceed 10 rad/s (Gockenbach 1999).

The tuning also will most likely minimize the expected rate of failure of the system in question. The expected failure rate is determined by the Weibull distribution that normally depends on the spring mass and damper values. The tuning further ensures that the pass band frequencies are not amplified or tampered with by the system. The load mass should range from 0 to 20 (Gockenbach 1999).

Parameters of Body Block In Simulink

A subsystem refers to a group of elements that are independent and interrelated that comprise to form a unified part. A ground block refers to a block that connects all other blocks that have their inputs port not connected to other blocks. Simulink always issues warnings whenever simulation is run with blocks that have unconnected ports of input. The best way to prevent the warning is through usage of ground blocks. The signal a ground block outputs or sends out is of the same type of data with the port which the ground block connects. This block can handle all types of date that simulink can support, for instance the fixed-point types of data and the enumerated types of data (Rouleau 2009).

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The environment lock, typically known as the machine environment block allows viewing and altering of the settings relating to the mechanical environment for a chosen machine in the model. A machine in this case refers to the sim-mechanics block diagram that is usually complete and connected but is distinct from other sim-mechanics block diagrams that are complete. The environment blocks are used to connect different sub machines that may comprise to form a machine. The sub machines are should contain at least one ground block. For the sim-mechanics model to be termed valid, it is required that one ground per machine should be connected to a machine environment block. The settings that the environment block determines include simulation of the machine, interpretation of the mechanical constraints, linearization of the simulation and what criteria will be used to determine whether the machine should be displayed in visualization or not (Chapman 2008).

The double suspended mass spring damper system depicts how the sim-mechanics can be used in the forward and inverse dynamics analysis. The model helps demonstrate the criteria to specify a point motion, whether position or velocity and also helps in measuring the force that is needed to generate the motion. The model measures the force that is produced by the damper and joint spring blocks. It also enables generation of the motion signal as facilitated by the integrator blocks. The recommended action is definition of the acceleration signal and making the integration twice. The positions should be specified to avoid problems that may arise if derived twice. This is because the derivate block most likely produces infinite derivate during the initial stages (Gockenbach 1999).

What Is SG, CS1 CS2

The model also helps in definition of bodies in the adjoining coordinates. The CSI position is usually (000) in the adjoining coordinates system while other coordinates remain in level with the CS1.This definitely will allow block copying and connections to other joints free from modification. Using the adjoining coordinates to define bodies usually helps to create systems that are reusable. The adjoining coordinates are visualized once the body block is opened.

Acceleration Graph

The bar graph here represents all the elements in a matrix as a single bar. The bars are normally distributed along the x-axis where each element in the columns is drawn in different locations contrary to the row where the elements are drawn or classified in the same location. The fist bars represent the first row of the Y-axis.

Advantages of Matlab

Matlab is easier to use mostly to the beginners who are doing their computer programming for the first time. The ease to use emanates from the interpreted language used. This ranges from the wide usage of the program. The program is used to evaluate expressions that are based on a command line hence is used to discharge the prewritten programs. Ease of writing or developing a program can be enhanced by the matlab debugger that enables prototyping of newer programs. There are also many program development tools that make the program usage easier. These are extensive demos, integrated debugger and worksspace browser (Chu 2010).

Matlab is composed of a library that consists of predefined functions which provide tested solutions to many of the tasks that are technical. This library of functions builds the basic language used by matlab. Matlab also comes with toolboxes that are specifically developed to solve problems in specific areas, for instance standard toolboxes that aid in signal processing, communication, processing of the image and control systems. Other matlab support programs are shared in the matlab website (Chu 2010).

This program is supported by various computer systems creating an independent platform this enhances the flexibility of running all the programs in all the platforms, for instance windows 2000, Linux etc. This caters for the needs and preferences of the user which change often. Once needs have changed, shifting from this platform to the other will be easier and with no worry of the programming not running (Chu 2010).

Matlab uses tools that allow construction of a graphical user interface for the programs better suited by the user. This gives the programmer the capability to design data analysis programs that can be executed by the inexperienced users. Compared to other computer languages, matlab is made up of integrated imaging and plotting commands. These commands enable the plots and images to be displayed on all graphical output devices that are supported by the computer being run by matlab (Chapman 2009).

This helps in visualizing technical data. It also enables one to carry out aloof o tasks given the workbenches and numerous add-ons it contains. This helps in doing calculations without necessarily writing a spreadsheet or using another program. The program also consists of well-written manuals. This aids in the ease of using it as well as seeking for help in cases where it is difficult to execute a certain program. The manuals provide flexibility and security. The users of matlab are many hence sharing of free codes is enhanced (Chapman 2009).

The workflow of matlab differs from all others in that the central interaction mainly occurs through a console and script. Commands in matlab are executed and written in the console. Another option is bundling them together into a script that can be repeated and reproduced (Chu 2010).

Disadvantages of Matlab

Slow processing performance as is a limitation to interpreted languages. The execution speed is delayed because the computer running the specified program is faced with the obligation of analyzing and interpreting code before execution. This is contrary to when the language is compiled where the whole code is first analyzed efficiently and processed before the application is distributed. This problem of delayed execution can be mitigated through structuring the matlab program so as to improve the performance of the code and through the application of JIT compiler (Chu 2010).

Matlab is considered as cost effective to firms or business but is relatively expensive when considering individual purchases. The business gain from the less cost due to the limited time that a scientist requires to develop a program that is working. However, Matlab has a less costly student edition that many students use for familiarizing themselves with the language (Chapman 2009).

Comparison of Matlab to GNU Octave

GNU Octave is also a highly interpreted language whose main obligation is to compute numerical data. The capabilities of this language range from the linear to nonlinear programs and provision of extensive graphics to enable data manipulation and visualization. It can be used in writing both the interactive and non interactive programs using the interactive command interface line. It is usually used under the GNU general public license which has declared its usage free (Eaton 2012). This program has been built in a manner compatible with the matlab hence has a lot of features it shares with matlab. Some of those features include use of matrices as the principle type of data, availability of built in support for the case of complexity in numbers, extensive math and library functions that are in-built and the widely covered user defined functions.

However there are also differences that exist between the two, for instance, some of the c-based programs like the C ++ are supported in the octave, it doesn’t require creation of new variables to enable referencing of elements. Octave provides more accurate results than the matlab in that in the case where the variable type is single, octave computes the mean using the single quotes and not the double domain used by the matlab.

Octave enables prefixing of comment lines using the # and the % characters which are not to matlab (Eaton 2012). Octave is generally described as free software by the licensing body regulating its distribution while the matlab is a proprietary program that is licensed to the owner. This gives the copyright holder of patent owner the exclusive rights to sell it. The graphic user interface of the matlab is rather complicated and less flexible as compare to octave. This gives the matlab the capability to execute the nested loops a little faster than the octave. There is the solution of the slow loops. The most appropriate solution is to replace the loops with modules that are executed or developed as C. It is also faster to use extensions like a++ instead of ‘a=a+1’ as advocated by the matlab.

Conclusion

Matlab makes it easier to do the numerical computations and representing them in graphs and other visual decoders. Developing the double mass spring damper with the knowledge of the model will be more accurate when using the programming language contrary to doing it manually. It is therefore recommended that matlab provides the accuracy as it has been tested and proven. Matlab rather can be effective if used without some supportive programs also called add-ons. Some of these add-ons are inclusive of the simulink, c++ and java. Matlab has also been viewed as having many advantages over all other programming language soft ware. It is seen as a faster way of solving all the solutions relating to simulation and providing the basis for such. When building a double mass spring and damper system, there is all the reason to use matlad to ensure effectiveness and accuracy. However there is need to do more research on the matlab soft ware and other related programs to help improve and get more information on the updates.