PHYSICS 321 - Classical Mechanics I

Spring 2007

Homework Set #6 (due 2/28/07)

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 w_a and w_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 w_b - w_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 v vs x phase plot). And 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?).

Now the oscillator is attached to an external driving force varying harmonically with time as F_ocoswt, where F_o = 1.0 N and w = 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 w 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?