karmonkey98k
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John Taylor "Classical Mechanics" Chapter 5, Problem 29
An undamped oscillator has period t(0)=1 second. When weak damping is added, it is found that the amplitude of oscillation drops by 50 percent in one period r1. (the period of the damped oscillations defined as time between successive maxima t1=2pi/w1) (w1=angular frequency). How big is B (damping constant) compared to w(0)? What is t1?
For undamped osc: x(t)=C1e^iw(o)t+C2e^-iw(o)t
For underdamping: w1=root(w(o)^2-B^2)
for weak damping: B<w(o)
well, the answers are t1=1.006 sec and B=0.110w(o). But I don't know how they arrived at those specific answers. How could you get those two numbers? May sound too general, but I just don't know how you could get numerical answers in general in this prob, from what we have.
Homework Statement
An undamped oscillator has period t(0)=1 second. When weak damping is added, it is found that the amplitude of oscillation drops by 50 percent in one period r1. (the period of the damped oscillations defined as time between successive maxima t1=2pi/w1) (w1=angular frequency). How big is B (damping constant) compared to w(0)? What is t1?
Homework Equations
For undamped osc: x(t)=C1e^iw(o)t+C2e^-iw(o)t
For underdamping: w1=root(w(o)^2-B^2)
for weak damping: B<w(o)
The Attempt at a Solution
well, the answers are t1=1.006 sec and B=0.110w(o). But I don't know how they arrived at those specific answers. How could you get those two numbers? May sound too general, but I just don't know how you could get numerical answers in general in this prob, from what we have.