a) Suspension system of a car. Finding the transfer function F₁(s) = Y(s)/R(t) and F₂ (s) = Q(s)/R(t),consider the initial conditions equal to zero.car chassiswwwK₂M₂1Tire M₁K₁B₁y(t)= outputq(t)r(t)= inputWhere [r, q, y] are positions, [k1, k2] are spring constants. [B₁] coefficient of viscous friction, [M₁, M₂]masses.b) Find the answer in time q(t) of the previous system. With the following Ns values: M₁ = 1 kg, M₂ = 0 kg,k₁ = 4 N/m, k₂ = 0 N/m, B₁. = 1 Ns/m, considered m a unit step input, that is, U(s) = 1/s

Given: To find: Transfer function

a) Suspension system of a car. Finding the transfer function F₁(s) = Y(s)/R(t) and F₂(s) = Q(s)/R(t), consider the initial conditions equal to zero. car chassis M₂ K₂ Tire M₁ K₁ B₁ y(t)= output q(t) r(t)= input Where [r, q, y] are positions, [k1, k2] are spring constants. [B₂] coefficient of viscous friction, [M₁, M₂] masses. b) Find the answer in time q(t) of the previous system. With the following Ns values: M₁ = 1 kg, M₂ = 0 kg, k₁ = 4 N/m, k₂ = 0 N/m, B₁. = 1 Ns/m, considered m a unit step input, that is, U(s) = 1/s

a) Suspension system of a car. Finding the transfer function F₁(s) = Y(s)/R(t) and F₂(s) = Q(s)/R(t), consider the initial conditions equal to zero. car chassis M₂ K₂ Tire M₁ K₁ B₁ y(t)= output q(t) r(t)= input Where [r, q, y] are positions, [k1, k2] are spring constants. [B₂] coefficient of viscous friction, [M₁, M₂] masses. b) Find the answer in time q(t) of the previous system. With the following Ns values: M₁ = 1 kg, M₂ = 0 kg, k₁ = 4 N/m, k₂ = 0 N/m, B₁. = 1 Ns/m, considered m a unit step input, that is, U(s) = 1/s

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Similar questions

Get the equation of motion by drawing the free body diagram of the given systems. a) Get the system's transfer function and find the unit digit answer. Show all decals in detail. m = 1 kg b= 20 Ns/m k = 125 N/m F ww k b) get the transfer function of the system. X(s)/Pg(s) =? Show all decals in detail. resistance R k Pg massless piston area (A) capacitance
My Solutions > Lower Colorado River (Problem 11.12 in Chapra) The Lower Colorado River consists of a series of four reservoirs as shown in Fig. P11.12 in the textbook. Mass balances can be written for each reservoir, and the following set of simultaneous linear algebraic equations results: [ 13.422 0 00; -13.422 12.252 0 0; 0 -12.252 12.377 0; 00-12.377 11.797] * [C_1, c_2, c_3, c_4]' = [750.5, 300, 102, 30] where the right-hand-side vector consists of the loadings of chloride to each of the four lakes. The variables c_1, c_2, c_3, and c_4 are the resulting chloride concentrations for Lakes Powell, Mead, Mohave, and Havasu, respectively. Given this information, complete the following tasks: (a) Use the matrix inverse to solve for the concentrations in each of the four lakes. (b) How much must the loading to Lake Powell be reduced for the chloride concentration of Lake Havasu to be 75? (c) Using the matrix 2-norm (spectral norm), compute the condition number and how many suspect digits…
secondary spacecraft reference plane primary spacecraft primary orbit plane Once you fix the primary or target spacecraft (the selection of primary spacecraft is only a matter of context), the relative motion of the secondary spacecraft is governed by the following initial value problem: a" 2wy - 3w? a = fz; x (0) = *0, x' (0) = x, y" + 2wa' = fy; y (0) = Yo, Y (0) = % 2' + w? z = fa; z (0) = 20; z' (0) Where w stands for the mean angular velocity of the primary spacecraft within its orbit plane. Also, fy represents the differential acceleration on the secondary spacecraft. fz x (t) Assuming there is no external force acting on the secondary spacecraft, use Laplace Transform to determine its position y (t) in the space. Your z (t) answer will be in terms of w and the set of intial conditions. Hint: The z part of the given IVP is a second order IVP by itself. Therefore it can be solved for z using Laplace Transform. For each of the first two differential equations (from the top), begin…
4. For the fluid system in Fig 6 construct the linear graph, identify the state variables, and derive the state equations. The output variables are the pressure p₁ and på at the tanks. C₁ Aut I,R 0,01) - Figure 6: An fluid system R₂ V (t) ww Rs ERL L V (1) Figure 7: A tuning circuit for radio
O 1::09 O [Template] Ho... -> Homework For the system shown in figure below, Find the range of K for stable system. R K(s + 2) C s(s +5)(s² + 2s + 5) II
Please
The state transmission matrix of the system whose state-space [3²₁] = [0²2 J]+[]u a. b. C. O 0 cosh at c. Ø(t) = [ a sinh at/a cosh a. ¢(t) = [sinhat cosh at a. Ø(t) = [a cosh at sinh at b. Ø(t) = [a [a cosh at a sinh at sinhat cosh at] sinhat/a] cosh at [/a] sinh at/a] a cosh at sinh at att cosh at
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): A. Use Laplace transform of the differential equation to determine the transfer function of the system.
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?
Represent the translational mechanical system shown below in state space, where x3(t) is the output. State variables ニュ=X 3 = X2 Let -4 = X2 Es = X3 E6 = X3 x1(t) x2(t) x3(t) 1 N-sim 1 N-sim 1 Nim 1 Nim 1kg 1kg 1 kg J1 J2 J3 Fit)
11. Consider a system that can be modeled as shown. The input x in (t) is a prescribed motion at the right end of spring k 2. Find X(s) the system transfer function Xeq(s)* m k₂ ww Xin The values of the parameters are m= 30 kg, k ₁=700 N/m, k 2= 1300 N/m, and b=200 N- s/m. Write a MATLAB script file that: (a) calculates the natural frequency, damping ratio, and damped natural frequency for the system; and (b) uses the impulse command to find and plot the response of the system to a unit impulse input.
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.