One-dimensional undamped harmonic oscillation

[Nusc]

A particle of mass m undergoes one-dimensional undamped harmonic oscillation due to a restoring force Fr = -kx. In addition the particle is subject to a constant external force Fext = Fo.
a) What is the differential equation that governs the motion of the particle?
b) what is the general solution for the position of the particle as a fxn of t?
c) What is the motion of the particle in the limit t - > infinity
d) If the oscillations are damped, what would be the motion of the particle in the limit t-> infinit?

a) d^2x/d^t^2 + kx/m = Fo/m
b) After applying the method of undetermined coefficients
x(t) = Acos(Wot + phi) + Fo/k

c) V = -Asin(Wot+ phi)(Wo)
t-> infiity , v - inifity?

d) If the former was undamped, how does introducing the damping constant change my solution?

Thanks

 

[mezarashi]

In (c), if the motion is undamped (also from the math) you see that there is no limit as t approaches infinity. The motion will remain forever oscillating between positive and negative A. If the motion is damped however, like any real spring you have, what is the motion of the spring after you leave it alone for a long time?

 

[Nusc]

Thanks a great deal for clarify the concepts.