Imagine that a block of mass 1 kg is attached to a ceiling by a spring with constant 5 kg/s? and a damper with constant 2 kg/s, and subjected to a force f(t), measured in Newtons (that is kgm/s²). Then its displacement from equilibrium in meters obey the equation dx + 2 +5x = f(t). dt dt2 Let f(t) = 3 eat and let initial conditions x(0) = x'(0) : = 1. Solve the DE for a = -2, and a = 2. [Hint: It is strongly recommended you solve for the general solution and IC-determined constants first, in terms of a. Then plug in to get the specific solution for each case.]
Imagine that a block of mass 1 kg is attached to a ceiling by a spring with constant 5 kg/s? and a damper with constant 2 kg/s, and subjected to a force f(t), measured in Newtons (that is kgm/s²). Then its displacement from equilibrium in meters obey the equation dx + 2 +5x = f(t). dt dt2 Let f(t) = 3 eat and let initial conditions x(0) = x'(0) : = 1. Solve the DE for a = -2, and a = 2. [Hint: It is strongly recommended you solve for the general solution and IC-determined constants first, in terms of a. Then plug in to get the specific solution for each case.]
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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![Imagine that a block of mass 1 kg is attached to a ceiling by a spring with constant 5 kg/s? and
a damper with constant 2 kg/s, and subjected to a force f(t), measured in Newtons (that is
kgm/s²). Then its displacement from equilibrium in meters obey the equation
dx
+ 2-
+ 5x = f(t).
dt
dt2
Let f(t) = 3 eat and let initial conditions x(0) = x'(0) = 1. Solve the DE for a = -2, and a = 2.
[Hint: It is strongly recommended you solve for the general solution and IC-determined constants
first, in terms of a. Then plug in to get the specific solution for each case.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F60ac7268-52d6-466f-850c-9576cf62e38d%2Ff1d54429-6750-41c4-9157-b7065925e0e5%2F76wd9i6_processed.png&w=3840&q=75)
Transcribed Image Text:Imagine that a block of mass 1 kg is attached to a ceiling by a spring with constant 5 kg/s? and
a damper with constant 2 kg/s, and subjected to a force f(t), measured in Newtons (that is
kgm/s²). Then its displacement from equilibrium in meters obey the equation
dx
+ 2-
+ 5x = f(t).
dt
dt2
Let f(t) = 3 eat and let initial conditions x(0) = x'(0) = 1. Solve the DE for a = -2, and a = 2.
[Hint: It is strongly recommended you solve for the general solution and IC-determined constants
first, in terms of a. Then plug in to get the specific solution for each case.]
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