PHYSICS 321 - Classical Mechanics I

Spring 2010

Homework Set #6 (due 3/3/10)

1. Thornton and Marion, problem 3-20. Do this problem by hand (using algebra), not using a computer. You will need to find the two angular frequencies (call them ω_a and ω_b) on either side of the resonance where the velocity amplitude has fallen to v_max/√2. The “full width” of the resonance is then defined as ω_b - ω_a.

2. Thornton and Marion, problem 3-21. You don’t have to use a computer. Just draw four phase paths (one from each quadrant of the x-dot vs x phase plot). Also calculate the asymptotic path (as t → ∞).

3. Thornton and Marion, problem 3-22.

4. Consider an oscillator consisting of a 0.2 kg mass attached to a spring with a force constant 5 N/m and immersed in a fluid that supplies a damping force represented by –bv with b = 0.3 kg/s. What is the nature of the damping (over?, under? or critical?).

Next the oscillator is attached to an external driving force varying harmonically with time as F_ocoswt, where F_o = 1.0 N and ω = 4 rads/s. What is the amplitude of the resulting oscillations?

What is the resonant frequency of the system i.e. what is the frequency ω that the driving force has to be tuned to in order to produce a maximum amplitude?

What is that amplitude?

What is the Q-value of the system?