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Simple Harmonic Motion

So this is a continuation from this thread: http://www.thestudentroom.co.uk/showthread.php?t=3229351

Our teacher brought in SHM. He said that if we were to do the experiment but this time pull the mass down the rule would oscillate, and the closer the supports where, i.e. L is shorter the higher the frequency of oscillation.

He passed this comment off without explaining why. So I decided to think about it.

From Stonebridge's comment in the previous thread, I decided to think of the rule as having a "spring constant" as we were talking about the stiffness as such of the rule. If this is the case I thought we could draw parallels to a mass on a string, in this case the angular frequency is directly proportional to the square root of the spring constant. Now when the supports are closer together the "spring constant" will be larger and hence the frequency. If this is even right, all I have done is explain it with the use of a mathematical formula, I am unsure why the frequency actually increases.

Any help is grateful.
A.S.
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Arbolus
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The way I think of it is that the up-and-down motion of the beam is effectively a standing wave, with a node where each of the supports is. Bringing them closer together reduces the maximum possible wavelength, and therefore increases the minimum possible frequency since the tension in the ruler remains constant.

That said, I think your spring constant method is equally valid. Moving the supports closer means that you have to deform the ruler more in order to pull the centre down by the same distance, which means that the force pulling it back will be greater.

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