A spring is such that a 4-lb weight stretches the spring 0.40 ft. The 4-lb weight is attached to the spring (suspended from a fixed support) and the system is allowed to reach equilibrium. Then the weight is started from equilibrium position with an imparted upward velocity of 2 ft/sec. Assume that the motion takes place in a medium that furnishes a retarding force of magnitude numerically equal to the speed, in feet per second, of the moving weight. Determine the position of the weight as a function of time.
A spring is such that a 4-lb weight stretches the spring 0.40 ft. The 4-lb weight is attached to the spring (suspended from a fixed support) and the system is allowed to reach equilibrium. Then the weight is started from equilibrium position with an imparted upward velocity of 2 ft/sec. Assume that the motion takes place in a medium that furnishes a retarding force of magnitude numerically equal to the speed, in feet per second, of the moving weight. Determine the position of the weight as a function of time.
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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Transcribed Image Text:1. A spring is such that a 4-lb weight stretches the spring 0.40 ft. The 4-lb weight is
attached to the spring (suspended from a fixed support) and the system is allowed to
reach equilibrium. Then the weight is started from equilibrium position with an
imparted upward velocity of 2 ft/sec. Assume that the motion takes place in a medium
that furnishes a retarding force of magnitude numerically equal to the speed, in feet
per second, of the moving weight. Determine the position of the weight as a function
of time.
2. Find the Laplace transform of
a) t² sinkt
b) tsinkt
3. Find the Inverse Laplace transform of :
5s-2
s² (s+2) (S-1)
S
b) (s²+²)(s²+b²) a² + b²,
a²b², ab 0
4. Use the Laplace Transform method to solve the given system
dx
dy
(a)
2x
- y = 6e³t,
dt
dt
2x-3x+
x(0) = 3,
d²₂ dy
dt² dt
dx
-x+
dt
dx
+ 3x +
- 4y + 3z = 0;
dt
dx
x(0) = 0,
(0) = 1, y(0) = 0, z(0) = 0.
dt
5. Find the Fourier series to represent a function of
a.)
f(x) = x + 1,
- 2 < x < 0,
= 1,
0<x<2
in the interval (-2,2).
b.) f(x) =cos cos
in the interval of (-, π).
(b)
dy
dt
y(0) = 0.
- 3y = 6e³t;
- y = 0,
dy
dt
dz-z = 0,
dt
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