Understanding the Oscillations of a Metronome

[ACE_99]

Homework Statement

Determine the equations governing the oscillations of a metronome.

The Attempt at a Solution

I believe that it has something to do with simple harmonic motion but I'm not sure where to start. Any help would be great.

 

[ehild]

How does a metronome look like?ehild

 

[ACE_99]

The metronome is one similar to the one in the link below.

http://www.concertpitchpiano.com/Wittner_metronome_mahogany.jpg"

 

[ehild]

Very good. Does not it look like a grandfather's clock but upside down? Yes, it performs oscillations, as a physical pendulum, and its motion can be considered as simple harmonic motion for small angles. The torque acting on the metronome when it is out of equilibrium tends to restore equilibrium and is equal to the angular acceleration times moment of inertia. For small angles, this leads to a differential equation identical with that for simple harmonic motion.

Here is a description of the mechanical pendulum from wikipedia:

"Mechanical metronomes

One common type of metronome is the mechanical metronome which uses an adjustable weight on the end of an inverted pendulum rod to control the tempo: The weight is slid up the pendulum rod to decrease tempo, or down to increase tempo. (The mechanism is also known as a double-weighted pendulum. There is a second, fixed weight on the other side of the pendulum pivot, hidden in the metronome case.) "
ehild