MTHE 225 Quiz: quiz 5 (10).pdf

• School: Queen's University
• Department: Mathematics & Engineering Courses
• Course: MTHE 225
• Professor: Gregory G Smith

Document Summary

Quiz 5a solutions: (5 marks) find the inverse laplace transform of f (s) = We wish to nd a, b, c such that. Multiplying both sides by s(s + 1)2, this equation becomes. 1 = a(s + 1)2 + bs(s + 1) + cs (1) Plugging in s = 0 gives a = 1. Plugging in s = 1 gives c = 1. To nd b, di erentiate both sides of equation (1) and plug in s = 1 to nd b = 1. = l {1} l {e t} l {te t} so f (t) = 1 e t te t: (5 marks) use laplace transforms to solve the initial value problem x + 4x + 29x = 0 , x(0) = 1 , x (0) = 2. Taking the laplace transform of both sides gives: s2x(s) s 2 + 4(sx(s) 1) + 29x(s) = 0 from which we obtain.