EBK SYSTEM DYNAMICS
3rd Edition
ISBN: 9780100254961
Author: Palm
Publisher: YUZU
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Chapter 2, Problem 2.25P
(a) Prove that the second-order system whose characteristic polynomial is
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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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- 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_forwardThe response to a unit step input (applied at time t = 0 s) of a system is shown in Figure Q2, determine the transfer function of this system from the step response graph. Amplitude 2.6 2.4 2.2 28 1.8 1.6 64 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0 Step Response 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 Time (sec) Figure Q2 Step response 1.2arrow_forward4 rad, = 0.5. On the complex plane, draw the root(s) of a 2nd order system with the following characteristics: W₁ = 4 radarrow_forward
- Mechanical Vibrations problemarrow_forwardQ2: a): In the system shown in figure below. Find the steady state error if the input r(t) = 1+ 2t C(t) e(t) r(t)- 10(s+1) s² (s+2)arrow_forwardDetermine the sensitivity of the overall transfer function for the system shown in figure below with respect to change in parameter; a- K b- H C(s) R(s) + w K s² + 23wn H Karrow_forward
- 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_forwardThe Routh-Hurwitz criterion to be used to determine the stability of a system with a characteristic equation given by 85 + 2s4 + 2s3 + 4s² + 11s + 10 Comment on the stability of the system. Neutral Stable Unstablearrow_forwardEquation of motion of a suspension system is given as: Mä(t) + Cx(t) + ax² (t) + bx(t) = F(t), where the spring force is given with a non-linear function as K(x) = ax²(t) + bx(t). %3D a. Find the linearized equation of motion of the system for the motion that it makes around steady state equilibrium point x, under the effect of constant F, force. b. Find the natural frequency and damping ratio of the linearized system. - c. Find the step response of the system ( Numerical values: a=2, b=5, M=1kg, C=3Ns/m, Fo=1N, xo=0.05marrow_forward
- For the system whose block diagram is shown in Fig.1, find the overall transfer function by using only one method of the followings: 1-Mason's Gain Formula. 2- Block diagram reduction techniques. R R G3 G1 G2 H1 Fig.1 H2arrow_forwardThe steady-state response is the part of the Total Response which does not approach infinity as time approaches infinity. True Falsearrow_forward3. Consider the state equation d x1 dt x2 with initial conditions 0 4 = -4 0 đ] ( x1 (7) x2 x1(0) ) ΧΟ x2(0) Determine the response x1(t) and x2(t) of the system by using the following two methods. (a) Determine the eigenvalues and eigenvectors of the state matrix. Derive x1(t) and x2(t) via eigenvector expansion. (b) Determine the state transition matrix using the series expansion eAt = I + At+ A2+2 A3+3 + +... 2! 3! to the fifth power. Derive x1(t) and x2(t) in terms of infinite series. (9)arrow_forward
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