EBK SYSTEM DYNAMICS
3rd Edition
ISBN: 9780100254961
Author: Palm
Publisher: YUZU
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Textbook Question
Chapter 2, Problem 2.62P
Use MATLAB to solve for and plot the impulse response of the following model, where the strength of the impulse is 5:
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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):
A. Use Laplace transform of the differential equation to determine the transfer function of the system.
Find the ditferential equation from the transfer of the function for the Giving
following system and draw the block diagram of the system.
x(s)
H(s)
u(s) 0.5s + 1
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?
Chapter 2 Solutions
EBK SYSTEM DYNAMICS
Ch. 2 - Prob. 2.1PCh. 2 - Solve each of the following problems by direct...Ch. 2 - Solve each of the following problems by separation...Ch. 2 - Prob. 2.4PCh. 2 - Prob. 2.5PCh. 2 - Obtain the Laplace transform of the following...Ch. 2 - Obtain the Laplace transform of the function shown...Ch. 2 - Prob. 2.8PCh. 2 - Prob. 2.9PCh. 2 - Prob. 2.10P
Ch. 2 - Prob. 2.11PCh. 2 - Obtain the inverse Laplace transform xt for each...Ch. 2 - Solve the following problems: 5x=7tx0=3...Ch. 2 - Solve the following: 5x+7x=0x0=4 5x+7x=15x0=0...Ch. 2 - Solve the following problems: x+10x+21x=0x0=4x0=3...Ch. 2 - Solve the following problems: x+7x+10x=20x0=5x0=3...Ch. 2 - Solve the following problems: 3x+30x+63x=5x0=x0=0...Ch. 2 - Solve the following problems where x0=x0=0 ....Ch. 2 - Invert the following transforms: 6ss+5 4s+3s+8...Ch. 2 - Invert the following transforms: 3s+2s2s+10...Ch. 2 - Prob. 2.21PCh. 2 - Compare the LCD method with equation (2.4.4) for...Ch. 2 - Prob. 2.23PCh. 2 - Prob. 2.24PCh. 2 - (a) Prove that the second-order system whose...Ch. 2 - For each of the following models, compute the time...Ch. 2 - Prob. 2.27PCh. 2 - Prob. 2.28PCh. 2 - Prob. 2.29PCh. 2 - If applicable, compute , , n , and d for the...Ch. 2 - Prob. 2.31PCh. 2 - For each of the following equations, determine the...Ch. 2 - Prob. 2.33PCh. 2 - Obtain the transfer functions Xs/Fs and Ys/Fs for...Ch. 2 - a. Obtain the transfer functions Xs/Fs and Ys/Fs...Ch. 2 - Prob. 2.36PCh. 2 - Solve the following problems for xt . Compare the...Ch. 2 - Prob. 2.38PCh. 2 - Prob. 2.39PCh. 2 - Prob. 2.40PCh. 2 - Determine the general form of the solution of the...Ch. 2 - a. Use the Laplace transform to obtain the form of...Ch. 2 - Prob. 2.43PCh. 2 - Prob. 2.44PCh. 2 - Obtain the inverse transform in the form xt=Asint+...Ch. 2 - Use the Laplace transform to solve the following...Ch. 2 - Express the oscillatory part of the solution of...Ch. 2 - Prob. 2.48PCh. 2 - Prob. 2.49PCh. 2 - Prob. 2.50PCh. 2 - Prob. 2.51PCh. 2 - Prob. 2.52PCh. 2 - Prob. 2.53PCh. 2 - 2.54 The Taylor series expansion for tan t...Ch. 2 - 2.55 Derive the initial value theorem:
Ch. 2 - Prob. 2.56PCh. 2 - Prob. 2.57PCh. 2 - Use MATLAB to obtain the inverse transform of the...Ch. 2 - Use MATLAB to obtain the inverse transform of the...Ch. 2 - Use MATLAB to solve for and plot the unit-step...Ch. 2 - Use MATLAB to solve for and plot the unit-impulse...Ch. 2 - Use MATLAB to solve for and plot the impulse...Ch. 2 - Use MATLAB to solve for and plot the response of...
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- The transfer function is the ratio of the Laplace transform of the input variable to the Laplace transform of the output variable, with all initial conditions equal to zero. True O Falsearrow_forwardExample For the system shown, the equations of motion are given by m₁x₁ + cx₁ + kx₁ Cx₂ = 0 m₂X₂ + CX₂ cx1 = F Use state space method to reduce the equation of motion into a system of 1st order differential equations. www m₁ m₂ farrow_forwardDraw the signal flow graph of the following block diagram, then find the transfer function using Mason's rule R a G₁ H₁ H₂ G₂ +arrow_forward
- For the unit step response shown find the transfer function of the system. 1.4 1.2 1.O 0.8 0.6 0.4 0.2 10 15 20 25 Time (seconds) Respansearrow_forward: Solve the following initial value problem by Laplace transformation: y" +9y=10e", y(0) = 0, y'(0)=0.arrow_forwardMultiple DOF SystemsA 2-D spring-mass, frictionless system has the following parameters:m1 = 72m2 = 27k1 = 381k2 = 183x1,0 = 0 mx2,0 = 1 mv1,0 = -1 m/sv2,0 = 0 m/s In MATLAB, solve numerically for x1(t) and x2(t).arrow_forward
- 2) Consider the transfer function of a system below. Please find the range of K for stability: K G(s) = (s + 3)(s + 8)(s + 10)(s + 1) + Karrow_forward4 Problem Find the Laplace transform fraction for the following function and rearrange it such that X(s)/F(s) is the only term on the left-hand-side: x(t) + 25wx (t) +w²x(t) = f(t) Assume the initial conditions are all zero, x(to) = x(to)= (to) = x (to) = 0 with initial time to = 0. Hint: Use the differentiation theorem.arrow_forwardlaplace transformarrow_forward
- 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_forwardA mechanical system is represented by two masses and three springs, where m, =12 kg, m, = 22kg, and spring constants k, = k, = kg = 15 N/m, as shown in the following figure. m2 Determine the largest eigenvalue of this mechanical system using the characteristic equation. а. Determine the smallest eigenvalue and the corresponding eigenvector using Inverse Power method. Given the initial eigenvector v(0)=(1 1 1)". Iterate until |ak+1 - 2x IS0.0005. b.arrow_forward04 Find the transfer function of the system shown by Mason's Rule, G₁ G₁ G₂ G3 H₁ G5 H₂ 95 Solve the following inverse transform Laplace transformations. 7s +15 C $²+2 Good luckarrow_forward
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