- #1
Blue Kangaroo
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Homework Statement
A lightly damped oscillator (mass, m, and spring constant,s, damping constant, b, with one end fixed) under
external harmonic force (F0cosωt).(i.e., Standard mass-spring system with lubricated damper, and driven by an external harmonic force.) Since it is lightly damped,γ<2ω0.
a.
Express the equation of motion (2nd order differential equation) for this forced oscillator
b.
Draw a vector diagram representing the equation of motion in general. Then, derive and express the resultant amplitude A and phase shift Φ. Make sure to draw arrows for vectors and the direction of the angle, φ.
.
Homework Equations
Fo/mcosωt = ψ +γψ + ωo2ψ
I'm not sure how to put dots to signify derivatives, but the first ψ is the 2nd derivative and the second one is the first derivative.
The Attempt at a Solution
I think the equation of motion is just as I wrote it previously. I need a little help with the vector diagram. I'm just having a little trouble understanding them. My professor is jusr OK and I don't really care for the book. I've uploaded some work I did on scratch paper, so if anyone could point out mistakes or give me some tips, I would greatly appreciate it. Thanks in advance.