- #1
Nusc
- 760
- 2
A particle of mass m undergoes one-dimensional damped harmonic oscillations with a damping constant gamma and a natural frequency omega nought. In addition the particle is subject to a time dependent external force given by:
Fext = f1t + f2t^2
a) What is the differential equation that governs the motion of the particle?
I found Xp(t) but I don't know what the homogeneous solution is because it doesn't specify if it's underdamped, overdamped, or critcally damped.
How do I know?
b) Determine what the "steady-state" solution will be at late times after all the transient motions have damped out.
So the particular solution will disappear because at t approaches infinity those terms with t will vanish. But I can't complete the question if I don't know the homogenous solution.
Fext = f1t + f2t^2
a) What is the differential equation that governs the motion of the particle?
I found Xp(t) but I don't know what the homogeneous solution is because it doesn't specify if it's underdamped, overdamped, or critcally damped.
How do I know?
b) Determine what the "steady-state" solution will be at late times after all the transient motions have damped out.
So the particular solution will disappear because at t approaches infinity those terms with t will vanish. But I can't complete the question if I don't know the homogenous solution.
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