# Which is more linear, a frictionless or slightly frictional pendulum clock?

1. Sep 20, 2004

### Loren Booda

A pendulum (clock) is moderately nonlinear for small angles of displacement. Is simple harmonic motion better approached by introducing a degree of friction into its works?

2. Sep 20, 2004

### Tide

I'm not sure what you mean by "moderately nonlinear" but, no, you won't change the way that the nonlinear "restoring force" behaves by adding damping. Perhaps you're confusing "nonlinear" with "unstable?"

Incidentally, the expression "simple harmonic oscillator" refers ONLY to a system with a linear restoring force and is often used in the small angle approximation to a pendulum.

3. Sep 20, 2004

### Loren Booda

Tide,

I helped a young man construct a 2-D pendulum whose bob traces out in sand its displacement vs time. It swings discernably for about ten cycles (a total of ~17 seconds), leaving both a record of its displacement and the number of periods. Is it a safe, albeit rough, approximation to use the linear period equation T=2pi(L/g)1/2 when such friction is involved?