A simple pendulum of length(adsbygoogle = window.adsbygoogle || []).push({}); loscillates

with an amplitude of 45°.

What is the approximate amount of 3rd harmonic

content in the oscillation of the pendulum?

NOTE:the numerical answer is apparently 0.0032.

I need to figure out how this was arrived at.

[tex]\hline [/tex]

As a starting point I'm using a power series:

[tex] m \frac{d^2x}{dt^2}+kx = \epsilon(x) = \epsilon_2x^2 + \epsilon_3x^3 + ...[/tex]

... and looking at the cubic term, so that

[tex] m \frac{d^2x}{dt^2}+kx = \epsilon_3x^3[/tex]

Specifically, I'm told to use the trial solution:

[tex]x = A cos \omega t + B cos 3 \omega t[/tex]

to find the ratio:

[tex]\frac{B}{A}[/tex] where A = the amplitude (45°)

where B is, ultimately, approximately equal to:

[tex] -\frac { \lambda A^3}{32\omega _0 ^2}[/tex]

and

[tex] \epsilon_3/m = \lambda[/tex]

[tex]\hline [/tex]

Here's where I'm stuck. What values do I use for:

[tex]\omega_0, \epsilon_3, m[/tex]

None of these are given in the problem statement??

Where the heck did B/A = 0.0032 come from?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# 3rd Harmonic Content for a Simple Pendulum?

**Physics Forums | Science Articles, Homework Help, Discussion**