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. (а) Write the definition of the Laplace transform of a function f(t).
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. (а) Write the definition of the Laplace transform of a function f(t).
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 2
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. (а)
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
e',
4.
Express f(t) =
in terms of unit step functions.
t>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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