Determine the equation of motion for the system shown in the figure below using the variables given in the figure. Note the mass moments of inertia of the load and the motor are J₁ and Jm, respectively. T(t) is the input torque, 0₁ (t) and 02 (t) are the output angles. Om Flexible Flexible shaft 01 Flexible shaft 02 shaft J1 Motor K1 K₂ K3 Jm Rigid B shaft T(t)

Mechanical system is shown in the figure. Torque, T(t), is given as an input which is applied ontothe disc and linear displacement of the cart, x(t), is given as an output for the system. The otherparameters and positive directions are given in the figure, also:M is the mass of the cart, J is the inertia of the disk, k is a linear and kT is a torsional springconstants, b is a linear damping constant, β is an angular displacement of the disk.a) At first, draw the necessary free-body diagrams (FBD’s) for the system. Then, identifying theforces with given elements (parameters) in the figure, write all elemental equations used inthe FBD’s. [ Note: Do not ignore the force which shows up on the contact point between thecart and the disc. Note 2: Please pay attention to the positive and negative signs that indicatethe direction.]b) Obtain the equation of motion (EoM) for the system in terms of input & output usingNewton’s Laws (i.e. *Continuity Eqn’s)c) Take Laplace transform of all…

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