c. The differential equation 1.25 u" + 20 u = 25 sin (t) +5 cos (t) describes a mass-on-a-spring system with no damping and external forcing. O TRUE O FALSE d. For the forced mass-on-a-spring system, the forcing frequency at which the amplitude of oscillations is largest equals the natural frequency of the unforced system. TRUE O FALSE e. The solution of the initial value problem mu" + yu' + ku и (to) %3D ио, и' (to) %3D u'о can be expressed as the sum u = v+ w, where v satisfies the initial conditions v (to) = 0, v (to) = u,, and w satisfies the initial conditions w (to) = uo, w' (to) = 0, and both v and w satisfy the same differential equation as u. O TRUE O FALSE
c. The differential equation 1.25 u" + 20 u = 25 sin (t) +5 cos (t) describes a mass-on-a-spring system with no damping and external forcing. O TRUE O FALSE d. For the forced mass-on-a-spring system, the forcing frequency at which the amplitude of oscillations is largest equals the natural frequency of the unforced system. TRUE O FALSE e. The solution of the initial value problem mu" + yu' + ku и (to) %3D ио, и' (to) %3D u'о can be expressed as the sum u = v+ w, where v satisfies the initial conditions v (to) = 0, v (to) = u,, and w satisfies the initial conditions w (to) = uo, w' (to) = 0, and both v and w satisfy the same differential equation as u. O TRUE O FALSE
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:c. The differential equation
1.25 u" + 20 u = 25 sin (t) +5 cos (t)
describes a mass-on-a-spring system with no damping and external forcing.
TRUE
O FALSE
d. For the forced mass-on-a-spring system, the forcing frequency at which the
amplitude of oscillations is largest equals the natural frequency of the unforced
system.
TRUE
FALSE
e. The solution of the initial value problem
mu" + yu' + ku
u (to) = uo,
u' (to) = u'o
%3|
%3|
can be expressed as the sum u = v+w, where v satisfies the initial conditions
v (to) = 0, v (to) = u,, and w satisfies the initial conditions w (to)
w' (to) = 0, and both v and w satisfy the same differential equation as u.
= u0 ,
TRUE
FALSE
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