Oscillations of a Ruler: Equation, Explanation & Answers

In summary, the conversation is about finding an equation that relates the number of oscillations of a plastic desk ruler to other factors such as length and force applied. The person asking the question has tried other equations but they did not make sense. They are looking for help in finding the correct equation and have been directed to look into the concept of a compound pendulum.
  • #1
thebosonbreaker
32
5
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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  • #3
Look into the ideas of a compound pendulum, that should help you.
 
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Likes thebosonbreaker
  • #4
  • #5
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.
 

Related to Oscillations of a Ruler: Equation, Explanation & Answers

1. What is the equation for the oscillations of a ruler?

The equation for the oscillations of a ruler is T = 2π√(I/mgd), where T is the period, I is the moment of inertia, m is the mass of the ruler, g is the acceleration due to gravity, and d is the distance between the center of mass and the axis of rotation.

2. Can you explain the concept of oscillations in more detail?

Oscillations refer to the back-and-forth motion of an object around a specific point or axis. In the case of a ruler, the oscillations occur when the ruler is pivoted at one end and released. The ruler then swings back and forth in a repetitive pattern, with the time it takes to complete one full swing being known as the period.

3. How does the mass of the ruler affect its oscillations?

The mass of the ruler affects its oscillations by influencing its moment of inertia. The greater the mass, the larger the moment of inertia, which in turn increases the period of the oscillations. This means that a heavier ruler will take longer to complete one full swing compared to a lighter ruler.

4. What factors can affect the period of oscillations in a ruler?

The period of oscillations in a ruler can be affected by several factors, including the length of the ruler, the mass of the ruler, the distance between the center of mass and the axis of rotation, and the strength of gravity. The equation for the period takes all of these factors into account.

5. How do the oscillations of a ruler demonstrate the concept of energy conservation?

The oscillations of a ruler demonstrate the concept of energy conservation because the total energy (kinetic + potential) of the system remains constant throughout the oscillations. As the ruler swings back and forth, its kinetic energy is constantly changing into potential energy and vice versa, but the total energy remains the same. This is due to the fact that there is no external force acting on the system, so the total mechanical energy remains conserved.

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