Re: What does reduced mass mean as regards SHM of springs?

Reduced mass in a two body system is calculated as

(Mass₁ * Mass₂)/(Mass₁ + Mass₂)

and much like center mass is useful energy and oscillation calculations. Without going into the boring detail of mechanics it often falls out of systems involving rotational energy or restoring forces (Hooke's Law) and/or gravity.

It is a mathematical convenience.

The reduced mass usually enters the equations when mass appears in denominators and terms are summed. For example:

1/X₁ + 1/X₂ =

(X₁ + X₂)/(X₁ * X₂)

In a Simple Harmonic Oscillator system there are normal modes (or resonances) that can be defined by a single frequency.

The basic equations of motion of a SHO can be expressed as a differential equations which is derived from the basic concept of balancing forces or energy. On the way to reducing the equations to an algebraic expression for frequency, one will usually add terms that have masses in the denominator and representing the term in the form a reduced mass will be useful.

Sincerely,

Tom "Nothing Reduced About His Mass" Cull