guaranteed approval loan or a no cosigner student loan in case your financial aid is not reinstated. When writing your awards letter request for reinstatement‚ NEVER‚ and I mean NEVER put the blame on someone else as to why you failed to meet the criterion. This is different than writing a letter of financial aid appeal because you need more money. Unless you got into a car accident that put you in a coma or were otherwise the victim of some crime that was out of your control‚ you should never blame
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ME 381 Mechanical and Aerospace Control Systems Dr. Robert G. Landers State Equation Solution State Equation Solution Dr. Robert G. Landers Unforced Response 2 The state equation for an unforced dynamic system is Assume the solution is x ( t ) = e At x ( 0 ) The derivative of eAt with respect to time is d ( e At ) dt Checking the solution x ( t ) = Ax ( t ) = Ae At x ( t ) = Ax ( t ) ⇒ Ae At x ( 0 ) = Ae At x ( 0 ) Letting Φ(t) = eAt‚ the solution
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given by m 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
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Calculus of Several Variables Exam 2009 -2 - Question 1 Use the Tables of Laplace transforms‚ along with the operational theorems‚ to find the Laplace transform of the following functions: (a) t(t + cos t)e−3t (b) (c) t 0 e−u sinh 2u du 4 − 4e2t t [4+2+2=8 marks] Question 2 (a) Write f (t) = 2t + 3‚ 0 ≤ t < 9 in terms of Heaviside functions. Find the Laplace −2‚ t≥9 transform of the function. (b) Use Laplace transforms to determine the solution y(t) of the following initial-value problem
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where ranges over all permutations of and is the inversion number of (Bressoud and Propp 1999). In linear algebra‚ the Laplace expansion‚ named after Pierre-Simon Laplace‚ also called cofactor expansion‚ is an expression for the determinant |B| of an n × n square matrix B that is a weighted sum of the determinants of n sub-matrices of B‚ each of size (n−1) × (n−1). The Laplace expansion is of theoretical interest as one of several ways to view the determinant‚ as well as of practical use in determinant
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function of t. dt 2 C d 2i 5. Find‚ by double integration‚ the area of circle x2+y2 = a2. 6. Prove that curl grad φ = o . 7. State the sufficient conditions for a function f(z) to be analytic. 8. State Cauchy’s integral theorem. 9. Find the Laplace transform of unit step function at t = a. 10. Find L-1 [ s+3 ]. s + 4s + 13 2 1 PART – B (5 x 16 = 80 marks) 2 − 2⎞ ⎛ 7 ⎜ ⎟ 11.(a).(i). Verify Cayley-Hamilton theorem for the matrix A = ⎜ − 6 − 1 2 ⎟ . ⎜ 6 2 −1⎟ ⎝ ⎠ Hence find its inverse
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fifty times larger than that of the Sun‚ would not‚ in consequence of its attraction‚ allow any of its rays to arrive at us; it is therefore possible that the largest luminous bodies in the universe may‚ through this cause‚ be invisible." -- Pierre Laplace‚ The System of the World‚ Book 5‚ Chapter VI (1798). Evolution of Stars 1. Clouds of Hydrogen begin condensing into more dense clusters due to gravitation. 2. Eventually the density gets high enough that the Hydrogen begins fusing into
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we have evaluated the importance of each criterion for your company. Based on this we have multiplied the ranking with the quantifier. So in the end the best possible result is 1‚ while 4 is the worst case. In the following section you will find the explanations for the weighting of the criteria. We evaluated the nationality and the marital status as least important‚ because these criteria have no significance about an applicant’s qualities. The criterion “Reason for leaving” has more importance
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(05PAF SMART CLASS) Read the Chapter of “Motivation” and answer the following questions. 1. Identify five different criteria by which organizations can compensate employees. Based on your knowledge and experience‚ do you think performance is the criterion most used in practice? Discuss. 5 Different Criteria by which organizations can compensate employees: Discipline Results Contribution Diligence Attitude Yes‚ we do think that performance is the criteria most used in practice. Because‚ most
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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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