Oscillations of a Ruler: Equation, Explanation & Answers

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The discussion focuses on finding an equation to relate the oscillations of a plastic desk ruler, treated as a cantilever beam, to factors like length and force applied. The original poster expresses difficulty in applying existing equations, such as T = 2π × √(L/g), which are typically for pendulums. Suggestions include exploring the concept of a compound pendulum to better understand the ruler's oscillatory behavior. A resource link is provided for further details on the cantilever beam dynamics. The conversation concludes with appreciation for the guidance received.
thebosonbreaker
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This probably has a very simple explanation, but I really need to know!

What I really want to know is, is there any equation that relates the number of oscillations to other factors such as length, force applied, etc. to a simple plastic desk ruler (image attached)?
(or) if there isn't one, how would I formulate an equation for it?

What I mean is that, if I hold one end down on the table and hold the other end down on the edge and then let it go, is there an equation that would tell me the number of times it moved up and down (oscillated) given other factors.

I have tried other equations, such as ( T = 2π × √(L/g) ) but the answer's don't make much sense. Although, I didn't really have any initial hope because most of them are for pendulums, not rulers.

I would really appreciate it if someone could help me.
Many thanks in advance.

DE-RULER.jpg
 
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Look into the ideas of a compound pendulum, that should help you.
 
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Aniruddha@94 said:
Look into the ideas of a compound pendulum, that should help you.
Yeah, that seems to be closer to what I'm looking for,
thanks for your help.
 
I do not have a good working knowledge of physics yet. I tried to piece this together but after researching this, I couldn’t figure out the correct laws of physics to combine to develop a formula to answer this question. Ex. 1 - A moving object impacts a static object at a constant velocity. Ex. 2 - A moving object impacts a static object at the same velocity but is accelerating at the moment of impact. Assuming the mass of the objects is the same and the velocity at the moment of impact...

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