Consider the initial value problem my" + cy' + ky = F(t), modeling the motion of a spring-mass-dashpot system initially at rest and subjected to an applied force where the unit of force is the Newton (N). Assume that m = 2 kilograms, c = 1 kilograms per second, k = 1 Newton (15 if 0 ≤ t ≤ 10 10 if t > 10. and velocity F(t) F(t), = Solve the initial value problem, using that the displacement y(t) and enter y' (t) remain continuous when the applied force is discontinuous. Find the value of y at 4π √7 y( 4π into the blank below. Keep two decimal places in your answer.
Consider the initial value problem my" + cy' + ky = F(t), modeling the motion of a spring-mass-dashpot system initially at rest and subjected to an applied force where the unit of force is the Newton (N). Assume that m = 2 kilograms, c = 1 kilograms per second, k = 1 Newton (15 if 0 ≤ t ≤ 10 10 if t > 10. and velocity F(t) F(t), = Solve the initial value problem, using that the displacement y(t) and enter y' (t) remain continuous when the applied force is discontinuous. Find the value of y at 4π √7 y( 4π into the blank below. Keep two decimal places in your answer.
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:Consider the initial value problem my" + cy' + ky = F(t),
modeling the motion of a spring-mass-dashpot system initially at rest and subjected
to an applied force
where the unit of force is the Newton (N). Assume that
F(t),
m = 2 kilograms, c = 1 kilograms per second, k = 1 Newton
F(t) = {
J15
if 0 ≤ t ≤ 10
0 if t > 10.
Solve the initial value problem, using that the displacement
y(t)
and velocity
y' (t)
remain continuous when the applied force is discontinuous. Find the value of y at
4π
√√7
and enter
y (
4π
√7
into the blank below. Keep two decimal places in your answer.
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