Refer to Problem 4.91. Use MATLAB to obtain the transfer functions
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System Dynamics
- Consider the following rotational mechanical system, a. Apply the "by inspection" method in Laplace domain to write the system of equations that represents the dynamics of the system b. Solve for the output variable q1(s). Use Cramer's rule or the substitution method to solve for the output variable q1(s). c. Give the transfer function G(s) = 91(s)/T(s) 0₁ (1) T(1) J1 82(1) oför J2 oooo K₁ K2 oooo Darrow_forwardObtain the transfer functions X1(s)/U(s) and X2 (s)/U(s) of the mechanicalsystem.arrow_forward6. The electro-mechanical system shown below consists of an electric motor with input voltage V which drives inertia I in the mechanical system (see torque T). Find the governing differential equations of motion for this electro-mechanical system in terms of the input voltage to the motor and output displacement y. Electrical System puthiy C V V₁ R bac (0) T bac T Motor - Motor Input Voltage - Motor Back EMF = Kbac ( - Motor Angular Velocity - Motor Output Torque = K₂ i Kbacs K₁ - Motor Constants Mechanical System M T Frictionless Supportarrow_forward
- 1. Draw and write the force equation of the linear translational system shown, and find the transfer function at figure a. and b. . Set Mg = 0 for the transfer functions. B2 B M M K B flt) + Mg A) + Mg (a) (b)arrow_forward1. Write the mathematical equations for the mechanical system given. Also find the transfer functionX2(s)/F(s) of the given system.arrow_forward3) For the mechanical system shown in Fig. 1, write the force equations at each coordinate and then determine the following transfer functions: X(s) a) ; b) U(s) Y(s) U(s) Y(s) ; c) X(s) quarter mass of the car m₂ the suspension unsprung mass. m₁ tire stiffness ground motionarrow_forward
- For the rotational mechanical system shown, find the transfer function Ɵ1(s)/T(s) and Ɵ2(s)/T(s).arrow_forward2.9. The following mechanical system may be used to measure acceleration. Construct the block diagram model and find the transfer functions and . FF K, K2 X2 FIGURE 2-9arrow_forward2) Consider the spring-mass-damper system hanging down from a ceiling. Initially, the system is at rest. Then, we gently place another mass (M) on top the original one (m). First, please obtain the equation of motion of the mass m in the system (before we placed the other object). Assign the displacement references yourself and obtain the equation accordingly. From the equation of motion, please obtain the transfer function, G(s), between an external force on the mass m , f(t), and the displacement of the mass m, x(t). Then, please obtain the motion of the object M, using the transfer function G(s). Don't forget that G(s) belongs to the system shown on the top! To solve this, represent the force applied by the added mass (M) as a function of time. How would you describe the act of adding a mass as an external force input? Then solve for x(t). c = 10 Ns/m k = 50 N/m m = 5 kg M M = 25 kg F(s) G(s) X(s)arrow_forward
- 2. Duffing's equation is a model for a dynamic system that includes a damping term and a nonlinear stiffness term. It most notably describes dynamics of electrical systems, but it has a simple analog as a nonlinear vibrations problem. Derive the non-homogeneous Duffings equation below using Hamilton's Principle. Start from the definition of the kinetic energy of a unit mass, and the virtual work of the springs and damper. Note, the spring force terms are both derivable from an energy function. x+cx+kx+vx³ = F sin sin(at)arrow_forwardExample 2 ; Write the mathematical equations for the mechanical system given. Also find the transfer function X₂(s)/F(s) of the given system. K 0000 M₁ X₁ B M₂ f(t)arrow_forwardFind the transfer functionarrow_forward
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