Class

1

• Class 5 Jan. 22
• N Coupled Oscillators
• Clarifying comments on driven oscillators and
  resonance.
• Finish off 2 coupled oscillators
• N coupled oscillators.

2

• Announcements
• Homework 2 Due FRIDAY 2PM
• (at end of class or outside Olin 174)
• Office hours W 5-6 pm, Th 4-5 pm
• (none Friday)

3
Clarifying comments on Driven Harmonic
Oscillator Differential equation of motion (eq
4-7, p. 83) We proposed a solution of the
form (although we have not verified it by
direct substitution)
4
is driving frequency
Eq. 4-11 p. 85
5

• Claimed that maximum amplitude (resonance)
  occurred when driving w w0.
• While this is still a very useful rule of thumb,
  it is strictly speaking only true in the case of
  completely undamped oscillations (g 0).
• Frequency at which amplitude is max. (resonant
  frequency)
• wresonant wm lt w0.
• Lets look at some graphs

6
Graphs of A(w) vs. w
m 1 kg, k 1 N/m, w0 1 rad/sec, g 0.1 s-1,
F0 1 N
7
Graphs of A(w) vs. w
m 1 kg, k 1 N/m, w0 1 rad/sec, g 0.5 s-1,
F0 1 N
See also Fig. 4-6 p. 85