
239Harmonic Oscillator
© 2010 Taylor & Francis Group, LLC
where, in the last step, we have used the fact that ω = 2π/T. For n = 0 we see that
a
0
= F
0
(2ΔT/T).
Then Equation 7.97a gives our periodic pulse force:
FtF
T
T
T
T
T
T
ext
() sinsin/
0
22
2
2=+
+
∆∆ ∆
π
π
π
π
+
+
cos( )
sincos()....
2
2
3
33
ω
π
πω
t
T
T
t
∆
The first term is just the average value of the external force, and the second term is the Fourier
component at the fundamental frequency. The remaining terms are harmonics of the fundamental:
2ω, 3ω, and so on.
Equation 7.97a gives the response function x(t), which describes the motion of our pulse-driven
damped oscillator:
xt xt Ant
n
() () co