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Mechanical system is shown in the figure. Torque, MA is given as an input which is applied onto the disc and linear displacement of the cart, x(t), is given as an output for the system. The other parameters and positive directions are given in the figure, also: M is the mass of the cart,/ is the inertia of the disk, k is a linear and kris a torsional spring constants. b is a linear damping constant /3 is an angular displacement of the disk
a) At first, draw the necessary free-body diagrams (FBD's) for the system. Then. identifying the forces with given elements (parameters) in the figure, write all elemental equations used in the FBD's. [ Note: Do not ignore the force which shows up on the contact point between the cart and the disc. Note 2: Please pay attention to the positive and negative signs that indicate the direction] b) Obtain the equation of motion (EoM) for the system in terms of input & output using Newton's Laws (i.e. *Continuity Eqn's) c) Take Laplace transform of all elemental & continuity eqa's and EoM. Then, find the transfer function (TF) of the system. d) Draw the block diagram of the system using Laplace transforms of the equations in part (c). [Note: Start with the equation containing the highest derivative of the output] e) Simplify the block diagram using with "Block Diagram Algebra" or Analytical**" Method to find the IF. Compare your results which you obtained in part (c) & (e).
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