Homework Help: John Taylor Classical Mechanics Chapter 5, Problem 29

1. Oct 30, 2013

karmonkey98k

John Taylor "Classical Mechanics" Chapter 5, Problem 29

1. The problem statement, all variables and given/known data
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?

2. Relevant 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)

3. The attempt at a solution
well, the answers are t1=1.006 sec and B=0.110w(o). But I dont 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.

2. Oct 30, 2013

ehild

What is the equation for x(t) in case of a damped oscillator?

ehild