Item 4B Item 4B Rachel Reiser Maths C Rachel Reiser Maths C Question 1 ab1+f’(x)2 dx y = acosh(xa) If: coshx=12ex+e-x Then: cosh(xa) = 12(exa+e-xa) y = acosh(xa) ∴ y=a(exa+e-xa)2 y=a(exa+e-xa)2 dydx=f’x=ddxa(exa+e-xa)2 dydx=f’x=ddx12aexa+e-xa f’x=12a1aexa+-1ae-xa f’x=exa-e-xa2 f’x2=exa-e-xa22 f’x2=(12exa-12e-xa)(12exa-12e-xa) f’x2=14e2xa-14e0-14e0+14e-2xa f’x2=14e2xa-12+14e-2xa f’x2=14e2xa-2+e-2xa Assuming the catenary is symmetrical‚ the entire length of
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DEPARTMENT OF MATHEMATICAL SCIENCES FACULTY OF SCIENCE UNIVERSITI TEKNOLOGI MALAYSIA SSCE 1793 DIFFERENTIAL EQUATIONS 1. TUTORIAL 3 Use the definition of Laplace transform to determine F (s) for the following functions. a. f (t) = 5e5t . c. f (t) = sinh 4t. e. f (t) = g. f (t) = t‚ 5‚ 0 4. t e ‚ 0 < t < 2 h. f (t) = 0‚ 2 < t < 4 5‚ t > 4. f. f (t) = sin 2t‚ 0 < t < π 0‚ t > π. 2. Use the Laplace transform table to find F (s) for the given function. a. f (t) = 2 sin t + 3 cos 2t. c
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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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the mechanical side and spring action provided by the synchronous tie wherein power transfer is proportional to sin d or d (for small d; d being the relative internal angle of machines). 3. Because of power transfer being proportional to sin d‚ the equation determining system dynamics is nonlinear for disturbances causing large variations in angle d. Stability phenomenon peculiar to non-linear systems as distinguished from linear systems is therefore exhibited by power systems (stable up to a certain
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Symbolic processing is the most powerful feature of matlab. We can solve even most complex equations very easily in matlab that are very difficult to solve by hand. Matlab performs symbolic processing to obtain answers in the form of expressions. Symbolic processing is the term used to describe how a computer performs operations on mathematical expressions. To improve engineering designs by modeling it with mathematical expressions that do not have specific parameter values are very difficult to
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VIKRAM KUMAR ABM10014 SUJIT PATEL ABM10016 SUMAN PGP28388 DHWITI JHAVERI PGP29126 HARI KRISHNA PGP29127 RAGHAV BHAIA PGP29128 ANSHUMAN SHARMA PGP29146 DIVYA ANAND PGP29160 PAWAN XAXA PGP29174 INDIAN INSTITUTE OF MANAGEMENT LUCKNOW TABLE OF CONTENTS
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accurate fit‚ I would propose creating a system of equations. Before jumping to far ahead‚ we need to make it clear the equation we are going to be analyzing. We will use the equation given to us by the polynomial trend line which is: y= ax2 + bx +c and the reason that we are using this equation is because of the fact that the R2 value is 0.9955. The closer the R2 value is to 1 the better it will fit the graph. We will rearrange the equation y= ax2 + bx +c so that we can solve for the unknowns
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A Honda Civic travels in a straight line along a road. It’s distance x from a stop sign is given as a function of time t by the equation‚ where and. Calculate the velocity of the car for each of the time given: (a) t = 2.00s; (b) t = 4.00s; (c) What will be the time when the acceleration is equal to zero? Solution: By getting the derivative of the distance as a function of time we can get the velocity as a function of time. Substitute the values of α and β
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CVEN9802 Structural Stability Beam Columns Chongmin Song University of New South Wales Page 1 CVEN 9802 Stability Outline • Effective Length Concept • Beam-Column with Distributed Load • Column with Imperfection • Southwell Plot • Column Design Formula Page 2 CVEN 9802 Stability Fundamental cases of buckling PE EI 2 L 2 2 2.045 EI P 4 EI Pcr cr 2 L2 L 2 Pcr 2 EI 4L 2 PE 2 EI L2 Page 3 CVEN 9802 Stability What is
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nonlinear ordinary differential equations using numerical method. To understand the 4th order Runge Kutta method and its applications. Problem statement Steel ball bearing radius 0.02m‚ ρ = dT 7800kg/m3 A T 4 Ta4 mC dt The radiation equation is The convection equation is Assumed T0= 1200K and Ambient temperature‚ Assumed that all heat transfer in radiation and convection only. Mathematical model Combining both convection and radiation equation to form a new rate of
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