Question 65 – A differential equation is given as y” + 5y’ + 6y = 0, y(0) = 2 and y’(0) = 3. By using Laplace transform, an engineer has correctly produced the equation L {y} = (2s + 13) / [(s + 2)(s + 3)] = A / (s + 2) + B (s + 3). (a) Find the values of A and B. (b) The inversed Laplace transform of 1 / (s + a) is given by exp (-at) where a is a constant. If the statement : L {y} = 9 L { exp (-2t) } - 7 L { exp (-3t) } is correct, find the equation of y as a function of t as a solution to the differential equation stated in the beginning of this question. When L {d} = 9 L {b} - 7 L {c}, then d = 9b - 7c with b, c and d are unknowns.
Answer Posted / kang chuen tat (malaysia - pen
Answer 65 – (a) Let (2s + 13) / [(s + 2)(s + 3)] = [A (s + 3) + B (s + 2)] / [(s + 2)(s + 3)]. Then 2s + 13 = As + 3A + Bs + 2B = (A + B)s + (3A + 2B), then A + B = 2 and 3A + 2B = 13. Let 2A + 2B = 4 as first equation by doubling A + B = 2 and 3A + 2B = 13 as second equation, the difference of first and second equations will produce A = 9. When A = 9, B = 2 - A = 2 - 9 = -7. (b) Let d = y, b = exp (-2t) and c = exp (-3t), then y = 9 exp (-2t) - 7 exp (-3t). The answer is given by Kang Chuen Tat; PO Box 6263, Dandenong, Victoria VIC 3175, Australia; SMS +61405421706; chuentat@hotmail.com; http://kangchuentat.wordpress.com.
Is This Answer Correct ? | 0 Yes | 0 No |
Post New Answer View All Answers
Hi, I am preparing for Indian Forest Service (UPSC). Can you please help me to get previous years question papers (Chemcial Engineerign) (atleast 5).
Is there any way to slow coke formation in ethylene furnaces?
Are there any special considerations to be taken into account for combusting ammonia?
Is there a handy way to determine if a horizontal pipe is running full if the flow rate is known?
Explain under what circumstances are vortex flowmeters the most accurate?
How i can calculate heat transfer in reactor at unsteady state and what data should i have? I want equation and process to calculate it? As there is steam or brine in jacket
Can any one send me the sample test papers of IOCL entry exam to be held on 6th july 2008. Also plz send the interview questions that cud probably be asked........i wud be highly obliged if u can send a few test paers and other stuff @ inderjeetd@gmail.com.........Inderpreet
List the advantages and disadvantages of a pfr?
What is a good method of analyzing powders for composition?
what is the apt definitions for apparent power ,active power and reactive power?and explanation about different types of lamps?
What is the procedure to estimate the friction factor involved in heat exchanger tubes?
We are having proplem with the persperation smell in ETT/ECHO room in our cardiac hospital.The 2 Ton of AC is not conditioning the environment. We have to use exhaust fan to through out of the room bad air. Could anyone suggest how to coup with this effectively using chemical engineering. Any permanent solution to neutralise the bad smell.The Air freshners are not doing enough instead making a bad odour.
Explain the functioning of a three-way catalytic converter.
Why do we apply on iron articles?
How can wet carbon dioxide be responsible for a corrosion problem in iron-containing metals?