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A velocity of a vehicle is required to be controlled and maintained constant even if there are disturbances because of wind, or road surface variations. The forces that are applied on the vehicle are the engine force (u), damping/resistive force (b*v) that opposing the motion, and inertial force (m*a). A simplified model is shown in the free body diagram below. From the free body diagram, the ordinary differential equation of the vehicle is: m * dv(t)/ dt + bv(t) = u (t) Where: v (m/s) is the velocity of the vehicle, b [Ns/m] is the damping coefficient, m [kg] is the vehicle mass, u [N] is the engine force. Question: Assume that the vehicle initially starts from zero velocity and zero acceleration. Then, (Note that the velocity (v) is the output and the force (w) is the input to the system): 1. What is the order of this system?

The following EOMs describe the behavior of a dynamic system ( à = -K₁a + din b = K₁a - K₂b K₂b - K3c = ċ Assume K₁, K2, K3 are constant, and din is the input. A. How many states does this system of equations have, and why? B. Write the state space form of the system as x = Ax + Bu. You will have to define your state vector and input vector. Clearly identify the matrices. C. Assume the desired output of the system is the vector y that consists of a and K₂b as individual elements. Write the output equation in the form of y = Cx + Du. Clearly identify the matrices.

I need only (C) which means the last question please only is to be solve. thank you

2. Find the equation(s) of motion of the following system. How many DOF does this system have? The displacement of the mass is measured from the position where the spring is unstreched. Is this system linear or nonlinear? Define the state variables and express the equation(s) of motion in state form. Gravity should be included and the Coulomb friction coefficient of the rough ground is u. F,(0 x,(t) Friction, u

diagram, F, is the input force exerted on the cart by the voltage applied to the motor, m, is the mass of the cart. The encoder is used to keep track of the position of the cart on the track. Cart Encoder Mater March 7, 2023 Track X Figure 5: Free body diagram of the cart (ignoring friction) Using Figure 5 and basic Newtonian dynamics you can derive the equations governing the system. 3.3 Motor Dynamics The input to your system is actually a voltage to the cart's motor. Thus, you need to derive the dynamics of the system that converts the input voltage to the foren exertal on the cart. These are the dynamics of the motor. Figure 6 shows a diagram of the electrical components of the motor. Figure 6: Clasic armature circuit of a standard DC motor For this derivation of the motor dynamics we assume the following: • We disregard the motor inductance: IR, so we can use the approximation 0. • Perfect efficiency of the motor and gearbox: -- 1. The torque generated by the motor is proportional…

Lagrange's equation can be used to find the dynamic model of the robot. Select one: True O False

For the mechanical translation system below, find the force-voltage analogy and force-current analogy. Use the following values. K1 = 2 fv, = 1/2 M1 = 1+a %3D K2 = 2 fv2 = 4+b M2 = 5 K3 = 3+c fv3 = 3 a = 0 where a = 3rd digit of your student number %3D b = 5th digit of your student number b =7 C = 7th digit of your student number C = 5 For reference, the 1st digit of your student number is the leftmost number in your student number. Indicate your student number when solving problems.

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Please solve the following question. Note that the second picture is the solution of the question from the book, I just want to know the steps to reach it.

Find the differential equation of the mechanical system in Figure 1(a) To obtain the differential equation of motion of the mass and spring system given in Fig. 1. (a) one may utilize the Newton's law for mass and spring relations defined as shown in Fig. 1. (b) and (c) use f = cv for viscous friction, where v is the velocity of the motion and c is a constant. Z/////// k M F. F, F F F, F, k EF=ma F = k(x, - x,) = kx (b) (c) Figure 1: Mass-spring system (a), Force relations of mass (b) and spring (c)

Find the equation of motion for the system of Figure P1.6, and find the natural frequency. In particular, using static equilibrium along with Newton's law, determine what effect gravity has on the equation of motion and the system's natural frequency. Assume the block slides without friction. 00 x(t) m Frictionless A surface

answer completely please

As4.  This is my third time asking this question. Please DO NOT copy and paste someone else's work or some random notes. I need an answer to this question.   There is a mass attached to a spring which is fixed against a wall. The spring is compressed and then released. Friction and is neglected. The velocity and displacement of the mass need to be modeled with an equation or set of equations so that various masses and spring constants can be input into Matlab and their motion can be observed. Motion after being released is only important, the spring being compressed is not important. This could be solved with dynamics, Matlab, there are multiple approaches.

2. A model for an airplane's pitch loop is shown below. Find the range of K that will keep the system stable. Can the system ever be unstable for positive values of K? Controller Aircraft dynamics Commanded pitch angle + K(s + 1) Pitch angle s + 10 s2 + 0.6s + 9 (s + 4.85) 1 Gyro

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Figure Q3 shows one cart with a mass that is separated from two walls by two springs and a dashpot, where kı, k2 and ka are the first, second spring and dashpot coefficients, respectively. The mass, m could represent an automobile system. An external force is also shown as F(t). Only horizontal motion and forces are considered. F(t) is input and x2(t) is output. (a) Derive all equations related to the system (b) Construct the block diagram from equation in (a) (c) Obtain the transfer function of the system

1. The equations of motion of this system are ÿ + 3y + 4y - 32 - 4Z = 0 Ż +52 +6Z-5ý - 6y = f(t) * = A + Bū y = Cx+Dū Put these equations into state variable form and express the model as a matrix vector equation if output of the system is y. Energy storage element m1 m2 k₁ k₂ State variable *1=ý x₂ = Ż x3 = y x4 =Z k₁ my D k₂ C₂H m₂