Explanation Given: Ramp function is given by x ( t ) = m t ; m = slope of ramp . Concept Used: Laplace transform of function f ( t ) is defined as L ( f ( t ) ) = ∫ 0 ∞ e − s t f ( t ) d t Where f ( t ) is piecewise continuo function defined for all t ≥ 0 . Calculation: Ramp function is given by x ( t ) = m t ; m = slope of ramp Thus, the Laplace transform of ramp function is given by L ( x ( t ) ) = L ( m t ) ⇒ L ( x ( t ) ) = ∫ 0 ∞ e − s t m t d t Here, we use the concept of integration by Parts method using ILATE rule and the prefernce goes as I: Inverse trigonometric function L:Logarthmic function A:Algebraic Function T:Trigonometric function E:Exponential function ∫ f ( x ) ︸ I g ( x ) ︸ I I d x = [ f ( x ) ∫ g ( x ) d x − ∫ { d d x f ( x ) ∫ g ( x ) d x } d x ] ⇒ L ( x

3rd Edition

ISBN: 9780100254961

Author: Palm

Publisher: YUZU

See similar textbooks

Concept explainers

Thermodynamic Relations

Thermodynamics is the division of physics that deals with the transfer of any kind of energy, whether it be heat, temperature, or work, from one object to another.

Videos

Question

Chapter 2, Problem 2.4P

To determine

The Laplace transform of the ramp function.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 2, Problem 2.3P

Chapter 2, Problem 2.5P

Chapter 2 Solutions

EBK SYSTEM DYNAMICS

Ch. 2 - Prob. 2.1P Ch. 2 - Solve each of the following problems by direct...Ch. 2 - Solve each of the following problems by separation...Ch. 2 - Prob. 2.4P Ch. 2 - Prob. 2.5P Ch. 2 - Obtain the Laplace transform of the following...Ch. 2 - Obtain the Laplace transform of the function shown...Ch. 2 - Prob. 2.8P Ch. 2 - Prob. 2.9P Ch. 2 - Prob. 2.10P

Ch. 2 - Prob. 2.11P Ch. 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. 2.21P Ch. 2 - Compare the LCD method with equation (2.4.4) for...Ch. 2 - Prob. 2.23P Ch. 2 - Prob. 2.24P Ch. 2 - (a) Prove that the second-order system whose...Ch. 2 - For each of the following models, compute the time...Ch. 2 - Prob. 2.27P Ch. 2 - Prob. 2.28P Ch. 2 - Prob. 2.29P Ch. 2 - If applicable, compute , , n , and d for the...Ch. 2 - Prob. 2.31P Ch. 2 - For each of the following equations, determine the...Ch. 2 - Prob. 2.33P Ch. 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. 2.36P Ch. 2 - Solve the following problems for xt . Compare the...Ch. 2 - Prob. 2.38P Ch. 2 - Prob. 2.39P Ch. 2 - Prob. 2.40P Ch. 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. 2.43P Ch. 2 - Prob. 2.44P Ch. 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. 2.48P Ch. 2 - Prob. 2.49P Ch. 2 - Prob. 2.50P Ch. 2 - Prob. 2.51P Ch. 2 - Prob. 2.52P Ch. 2 - Prob. 2.53P Ch. 2 - 2.54 The Taylor series expansion for tan t...Ch. 2 - 2.55 Derive the initial value theorem: Ch. 2 - Prob. 2.56P Ch. 2 - Prob. 2.57P Ch. 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...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Recommended textbooks for you

Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY