- 2.2.1: Determine whether or not the following equations are linear or nonl...
- 2.2.2: Solve each of the following problems by direct integration: a. 4x =...
- 2.2.3: Solve each of the following problems by separation of variables: a....
- 2.2.4: Derive the Laplace transform of the ramp function x(t) = mt, whose ...
- 2.2.5: Extend the results of 2.4 to obtain the Laplace transform of t 2.
- 2.2.6: Obtain the Laplace transform of the following functions: a. x(t) = ...
- 2.2.7: Obtain the Laplace transform of the function shown in Figure P2.7. ...
- 2.2.8: Obtain the inverse Laplace transform f (t) for the following: a. 6 ...
- 2.2.9: Obtain the inverse Laplace transform f (t) for the following: a. 5s...
- 2.2.10: Use the initial and final value theorems to determine x(0+) and x()...
- 2.2.11: Obtain the inverse Laplace transform x(t) for each of the following...
- 2.2.12: Obtain the inverse Laplace transform x(t) for each of the following...
- 2.2.13: Solve the following problems: a. 5x = 7t x(0) = 3 b. 4x = 3e5t x(0)...
- 2.2.14: Solve the following problems: a. 5x + 7x = 0 x(0) = 4 b. 5x + 7x = ...
- 2.2.15: Solve the following problems: a. x + 10x + 21x = 0 x(0) = 4 x(0) = ...
- 2.2.16: Solve the following problems: a. x + 7x + 10x = 20 x(0) = 5 x(0) = ...
- 2.2.17: Solve the following problems: a. 3x + 30x + 63x = 5 x(0) = x(0) = 0...
- 2.2.18: Solve the following problems where x(0) = x(0) = 0. a. x + 8x + 12x...
- 2.2.19: Invert the following transforms: a. 6 s(s + 5) b. 4 (s + 3)(s + 8) ...
- 2.2.20: Invert the following transforms: a. 3s + 2 s2(s + 10) b. 5 (s + 4)2...
- 2.2.21: Solve the following problems for x(t): a. 5x + 3x = 10 + t 2 x(0) =...
- 2.2.22: Compare the LCD method with equation (2.4.4) for obtaining the inve...
- 2.2.23: Solve each of the following problems with the trial solution method...
- 2.2.24: Determine whether the following models are stable, unstable, or neu...
- 2.2.25: (a) Prove that the second-order system whose characteristic polynom...
- 2.2.26: For each of the following models, compute the time constant, if any...
- 2.2.27: Obtain the steady-state response of each of the following models, a...
- 2.2.28: Compare the responses of 4x + x = g(t) + g(t) and 4x + x = g(t) if ...
- 2.2.29: Obtain the response of the model 3x + x = f (t), where f (t) is an ...
- 2.2.30: If applicable, compute , , n, and d for the following characteristi...
- 2.2.31: The characteristic equation of a certain system is s2 + 10ds + 29d2...
- 2.2.32: For each of the following equations, determine the transfer functio...
- 2.2.33: Obtain the transfer functions X(s)/F(s) and Y (s)/F(s) for the foll...
- 2.2.34: Obtain the transfer functions X(s)/F(s) and Y (s)/F(s) for the foll...
- 2.2.35: a. Obtain the transfer functions X(s)/F(s) and Y (s)/F(s) for the f...
- 2.2.36: a. Obtain the transfer functions X(s)/F(s) and X(s)/G(s) for the fo...
- 2.2.37: Solve the following problems for x(t). Compare the values of x(0+) ...
- 2.2.38: Solve the following problems for x(t). The input g(t) is a unit-ste...
- 2.2.39: Solve the following problem for x(t) and y(t): 3x = y x(0) = 5 y = ...
- 2.2.40: Solve the following problem for x(t) and y(t): x = 2x + 5y x(0) = 5...
- 2.2.41: Determine the general form of the solution of the following equatio...
- 2.2.42: a. Use the Laplace transform to obtain the form of the solution of ...
- 2.2.43: Obtain the inverse Laplace transform of X(s) = 30 s2 + 6s + 34s2 + 36
- 2.2.44: Solve the following problem for x(t): x + 12x + 40x = 3 sin 5t x(0)...
- 2.2.45: Obtain the inverse transform in the form x(t) = A sin(t + ), where ...
- 2.2.46: Use the Laplace transform to solve the following problem: x + 6x + ...
- 2.2.47: Express the oscillatory part of the solution of the following probl...
- 2.2.48: Find the steady-state difference between the input f (t) and the re...
- 2.2.49: Invert the following transform: X(s) = 1 e3s s2 + 6s + 8
- 2.2.50: Obtain the Laplace transform of the function plotted in Figure P2.50.
- 2.2.51: Obtain the Laplace transform of the function plotted in Figure P2.51.
- 2.2.52: Obtain the Laplace transform of the function plotted in Figure P2.52.
- 2.2.53: Obtain the response x(t) of the following model, where the input P(...
- 2.2.54: The Taylor series expansion for tan t is tan t = t + t 3 3 + 2t 5 1...
- 2.2.55: Derive the initial value theorem: lims s X(s) = x(0+)
- 2.2.56: Derive the final value theorem: lim s0 s X(s) = limt x(t)
- 2.2.57: Derive the integral property of the Laplace transform: L t 0 x(t) d...
- 2.2.58: Use MATLAB to obtain the inverse transform of the following. If the...
- 2.2.59: Use MATLAB to obtain the inverse transform of the following. If the...
- 2.2.60: Use MATLAB to solve for and plot the unit-step response of the foll...
- 2.2.61: Use MATLAB to solve for and plot the unit-impulse response of the f...
- 2.2.62: Use MATLAB to solve for and plot the impulse response of the follow...
- 2.2.63: Use MATLAB to solve for and plot the step response of the following...
- 2.2.64: Use MATLAB to solve for and plot the response of the following mode...
- 2.2.65: Use MATLAB to solve for and plot the response of the following mode...

# Solutions for Chapter 2: Dynamic Response and the Laplace Transform Method

## Full solutions for System Dynamics | 3rd Edition

ISBN: 9780073398068

Solutions for Chapter 2: Dynamic Response and the Laplace Transform Method

Get Full SolutionsSystem Dynamics was written by and is associated to the ISBN: 9780073398068. Chapter 2: Dynamic Response and the Laplace Transform Method includes 65 full step-by-step solutions. This textbook survival guide was created for the textbook: System Dynamics, edition: 3. This expansive textbook survival guide covers the following chapters and their solutions. Since 65 problems in chapter 2: Dynamic Response and the Laplace Transform Method have been answered, more than 20406 students have viewed full step-by-step solutions from this chapter.