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

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ISBN: 9780073398068

Author: III William J. Palm

Publisher: MCG

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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.

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Chapter 2, Problem 2.4P

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The Laplace transform of the ramp function.

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Chapter 2 Solutions

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...

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