# Linear Simple Harmonic Oscillator: period a direct linear proportion to mass?

1. Feb 2, 2009

### charlatain

If a mass that hangs suspended vertically from a spring is increased, then won't the period increase as a direct linear proportion? (Because the larger mass has a greater inertia and will require a larger force and longer time to change the direction of motion on each oscillation?)

Some guidance would be greatly appreciated!!

Last edited: Feb 2, 2009
2. Feb 2, 2009

### adriank

A simple harmonic oscillator with spring constant k and mass m has angular frequency $\omega = \sqrt{k/m}$, so the period is $T = 2\pi/\omega = 2\pi\sqrt{m/k}$.

Thus, period is proportional to the square root of the mass.

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