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3. (а) Write the definition of the Laplace transform of a functionf(t). (Б) Use the definition to calculate L{t}. State an appropriate restriction on s.

3. (а) Write the definition of the Laplace transform of a functionf(t). (Б) Use the definition to calculate L{t}. State an appropriate restriction on s.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Pls Answer Question 3 part B

Suppose the same spring-mass system is now attached to a movable plank, which moves like the function 5 sin 2t for all t > 0. Adjust the initial value problem you wrote in part (a) to include this fact. Do not solve! 2. Find two linearly independent power series solutions of the differential equation (x + 2)y" + xy' – y = 0. 3. (a) Write the definition of the Laplace transform of a function f(t). (b) Use the definition to calculate L{t}. State an appropriate restriction on s. sin t, 0<t < 5 4. Express f(t) = in terms of unit step functions. e', t2 5 5. Using Laplace transforms, solve the IVP 1, 0<t < 1 0, y" + 9y = f(t), y(0) = 0, y'(0) = -1, where f(t) t>1
Transcribed Image Text:Suppose the same spring-mass system is now attached to a movable plank, which moves like the function 5 sin 2t for all t > 0. Adjust the initial value problem you wrote in part (a) to include this fact. Do not solve! 2. Find two linearly independent power series solutions of the differential equation (x + 2)y" + xy' – y = 0. 3. (a) Write the definition of the Laplace transform of a function f(t). (b) Use the definition to calculate L{t}. State an appropriate restriction on s. sin t, 0<t < 5 4. Express f(t) = in terms of unit step functions. e', t2 5 5. Using Laplace transforms, solve the IVP 1, 0<t < 1 0, y" + 9y = f(t), y(0) = 0, y'(0) = -1, where f(t) t>1
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