6. Consider the mechanical system shown in Fig. 8. Let V(t) be the input and the accelerationof the mass be the output. Derive the state equations and the output equation using lineargraphs and normal trees.BmV₁(t)Figure 8: A mechanical system with anacross-variable source

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Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

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A suspension system of Volvo articulated dump truck is to be modelled mathematically given the following data: keq = 10.5 MN/m, m = 30 tons, and c = 300 N-s/m. If the harmonic forcing function is 2000 cos 5t N with the initial displacement and velocity to be 0 and 30 m/s respectively, determine the steady state and total response 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?
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.
The figure that is attached illustrates a system in which a force F is applied to a mass m2 that is connected to another mass m1 via a spring and a damper, and mass m1 is connected to a wall via a damper. The equations of motion that govern the time evolution of the mass displacements, y1(t)and y2(t), are given below. A) Define 4 state variables of the system (xi, i = 1,…,4) as phase variables, and define the control input u. Convert the two equations of motion above into four 1st-order ODEs that are functions of the state variables and the control input.(b) Write the four 1st -order ODEs from part (a) in state-space form,x = Ax+Bu.
The block diagram given below; A) Reduce it B) G1(s)=2/s ; G2(s)=1/4s+2 ; G3(s)=4 ;H(s)=0.5 Given the values of the system; find the time constant, its natural frequency and damping rate and explain what kind of dynamic behavior it exhibits accordingly. C)Find the poles and zeros of the system according to the values in (B).Is the system stable? Find the unit step response (Inverse Laplace).
A certain mass is driven by base excitation through a spring (Figure P4.13). Its parameter values are m = 100 kg, c = 1000 N * s/m, and k = 10,000 N/m. Determine its peak frequency w_p, it’s peak M_p, and its bandwidth.
In the figure, a disk-shaped wheel of mass M and radius R rolls without slipping on a circular platform of radius 2L+R. The wheel is attached by a torsion spring to a pendulum of length 2L of mass m and moves with this pendulum.a) Derive the differential equation for the motion of the system given here.b) Find the natural frequency of the free motion of the system. L=2 [m], R= 0,5 [m], m=5 [kg], M= 65[kg], kb= 165 [Nm/rad] Note: There is no friction in this system
Find the natural response of the following spring–mass system with m=1,k= 1 and the initial position and velocity being both equal to 1. Please answer in typing format please
Suppose a spring with spring constant 7 N/m is horizontal and has one end attached to a wall and the other end attached to a 2 kg mass. Suppose that the friction of the mass with the floor (i.e., the damping constant) is 1 N⋅s/m a) Set up a differential equation that describes this system. Let x to denote the displacement, in meters, of the mass from its equilibrium position, and give your answer in terms of x,x′,x′′. Assume that positive displacement means the mass is farther from the wall than when the system is at equilibrium. b) Find the general solution to your differential equation from the previous part. Use c1 and c2 to denote arbitrary constants. Use t for independent variable to represent the time elapsed in seconds. Your answer should be an equation of the form x=… c) Enter a value for the damping constant that would make the system critically damped. ?Ns/m
Derive the governing differential equation for each system with the chosen generalized coordinate. SEE THE IMAGE BELOW Answers: 1. GDE: (5/2) mẍ + (5/4) kx = 0 2. GDE: (7/48) mL² ϴ [note: theta symbol has two dots above) + (3/8) cL² ϴ [ note: theta symbol has one dot above] + 5 kL² ϴ = 0
For the system shown in Figure, find: a) The system equation of motion in terms of θ b) The system natural frequency, ωn c) The system damping factor, ξ d)The system natural damped frequency
Figure Q1 shows a three-degree-of-freedom spring-mass system. If all the masses moveto the right direction;a.Construct the free body diagram and develop the equation of motion for each mass.b.Write the equation of motion for the system in matrix form such that it is completewith all parameter values.c.Estimate the natural frequencies of the system where the spring coefficient, k1 = k2= k3 = k4 = 127 N/m and the masses, m1 = m2 = m3 = 17 kg.d.Determine the mode shapes of the system. Assume x1=1 in modal vectorNote: No need to sketch the mode shape diagram

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6. Consider the mechanical system shown in Fig. 8. Let V(t) be the input and the acceleration of the mass be the output. Derive the state equations and the output equation using linear graphs and normal trees. B m V₁(t) Figure 8: A mechanical system with an across-variable source