Transfer Function General with order‚ linear‚ time invariant differential equation an dn(t)dtn+ an-1 dn-1c(t)dtn-1+…a0ct= bmdmrtdtm+bm-1dm-1rtdtm-1+…b0r(t) Where: c (t) is the output r (t) I is the input By taking the Laplace transform of both sides ansn cs+ an-1sn-1 cs+…a0cs+initial condition involving c(t) =bmsmRt+bm-1sm-1Rt+…b0Rs+initial condition involving r(t) If we assume that all initial condition are zero ansn+ an-1sn-1….+…a0cs=bmsm+bm-1sm-1+…b0r(s) Rs-→ bmsm+bm-1sm-1+…b0ansn+
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Calculate the Laplace Transform of a Function TerminologySolving the transformDiscontinuous FunctionsUsing Properties of Laplace Transforms Edited by Caidoz‚ Flickety‚ Zareen‚ Garshepp and 4 others The Laplace transform is an integral transform which allows a differential equation to be converted into a (hopefully) simpler algebraic equation‚ making it easier to solve. While you can use tables of Laplace Transforms‚ it is never a bad idea to know how to do the transform yourself. EditSteps
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power factor (numerical value and leading or lagging) if i g = 40 cos(5000t )mA. P= ‚Q= ‚ S = ‚ PF = ‚ leading/lagging (circle one) Problem 2: Basics of Laplace Transforms (10 pts.) Find L{t 2 e −2t + 10 sin( 3t + 45 o )} using only the Laplace transform pairs‚ the properties of the Laplace transform (not the ones in the formula sheet‚ just what you are given below)‚ and math identities that are provided below. a) sin(A+B) = sinAcosB + cosAsinB‚ b) 1 ω s L{e − at } = ‚
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( t ) = Ax ( t ) = Ae At x ( t ) = Ax ( t ) ⇒ Ae At x ( 0 ) = Ae At x ( 0 ) Letting Φ(t) = eAt‚ the solution is written as x (t ) = Φ (t ) x ( 0) The matrix Φ(t) is called the state transition matrix. The state transition matrix transforms the initial conditions. State Equation Solution Dr. Robert G. Landers Properties of State Transition Matrices State transition matrix evaluated at t = 0 Φ ( 0 ) = eA 0 = I Inverse of the state transition matrix Φ (t ) = e = (e
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x + c x + kx = F . Taking the Laplace transforms of the above equation (assuming zero initial conditions)‚ we have ms 2 X ( s ) + csX ( s ) + kX ( s ) = F ( s )‚ X ( s) 1 ⇒ = . 2 F ( s ) ms + cs + k Equation (1) represents the transfer function of the mass-spring-damper system. Example 2 Consider the system given by the differential equation y + 4 y + 3 y = 2r (t )‚ where r(t) is the input to the system. Assume zero initial conditions. The Laplace transforms yields‚ s 2Y ( s ) + 4 sY ( s ) + 3Y (
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Earthquake Preparedness Press Release to Los Angeles Area Bobby Dillion GLG/220 December 3‚ 2012 Phil Clifford‚ PhD. | How can my family be prepared for an earthquake? This question haunts countless residents in the Los Angeles area every day. Hopefully we here at the Earthquake Preparedness Center can shed some light on how you can protect your family. My name is Darin Fort and I am the Director of Earthquake Preparedness for Los Angeles. As with any danger‚ knowledge of the event
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Application of Laplace Transform The Laplace transform technique is applicable in many fields of science and technology such as: Control Engineering Communication Signal Analysis and Design Image Processing System Analysis Solving Differential Equations (ordinary and partial) Advantages of Laplace transformation A Laplace transformation technique reduces the solutions of an ordinary differential equation to the solution of an algebraic equation. When the Laplace transform technique is applied
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Austronesian Migration Theory propounds on the expansion of a group of people called the Austronesians from Asia into the Pacific by means of Taiwan 6‚000 years ago. It was a theory proposed by Peter Bellwood a professor of Archeology. The theory largely explains the similarities in culture‚ language and physical attributes in different countries in the most Asian countries. The Austronesian migrations began from the Chinese mainland‚ reaching Taiwan first in 3500 BC then the Philippines by 3000
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Grade Details There are 2 pages in this exam: Page: 1 2 1. Question: (TCO 4) A body moving with an acceleration having a constant non-zero magnitude must experience a change in: Your Answer: Speed acceleration velocity CORRECT weight Instructor Explanation: Remediation: Knight‚ Chapter 1.6 Points Received: 6 of 6 2. Question: (TCO 4) A ball is dropped from a 250 foot building. How long before the ball hits the ground
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Balanced Scorecard Report the strategy execution source november – december 2011 : vol 13 no 6 Sustainability Strategy Transforms the Enterprise By David Lubin‚ Chairman‚ Esty Sustainability Network‚ and Director‚ Palladium Group; Amy Longsworth‚ Partner‚ Esty Environmental Partners; and Randall Russell‚ Director of Research‚ Palladium Group Capitalism is a dynamic system for creating economic value. It continues to evolve as the world changes. What once were considered externalities in the
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