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The answers you're looking for can be rather complex....

Posted by John Elison (A) on January 10, 2007 at 17:56:51

In Reply to: DIY tone arm questions (mass, resonance, etc.)... posted by ER on January 10, 2007 at 13:05:34:

> how exactly do you calculate the resonance (plain english please)

If you know the cartridge's compliance at resonance and the tonearm's effective mass you may apply the following formula:

Resonance Frequency = 1000 / {2 x (pi) x Sqrt[C x (MC + EMA)]}

Where:
(pi) = 3.14159
C = Cartridge Compliance in mm/N
MC = Mass of Cartridge including mounting bolts in grams.
EMA = Effective Mass of Tonearm in grams
Sqrt[ ] = Square Root of everything inside brackets.

> what is the difference between "effective" mass and plain old mass?

There is significant difference, which is exactly as Mark Kelly explained.

Another way of looking at effective mass is from the spring mass model. The cantilever has a spring suspension and the cartridge and tonearm have mass. The spring suspension in conjunction with the mass interact to produce a resonance frequency. The effective mass of the system is the same as a point-mass that if placed directly at the spring would produce the same resonant frequency.

In other words, the total mass of a tonearm might be several hundred grams, but its effective mass might be only 12-grams. Take the following example of a tonearm:

Click on the link below for a thread that describes in detail how to calculate the effective mass of this tonearm.

> Where does the counter-weight figure into all of this, is everything behind the pivot point irrelevant?

No, everything behind the pivot is relevant and adds to the tonearm's effective mass. When you go through the calculations in the link below you will understand how everything figures in.

There is a lot involved in the questions you ask. Mark Kelly is an expert who knows the answers to your questions. However, it requires significant information and technical knowledge to answer your questions completely, which can be obtained from a thorough study of mechanics and dynamics.

Best regards,
John Elison

• Effective Mass and Moment of Inertia by Mark Kelly   (Open in New Window)

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