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

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

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