Finding how weight placed on a ruler affects its oscillation.

In summary, the conversation discusses an experiment involving a vibrating ruler and weights placed on its end. The idea is to measure the effect of different weights on the time of oscillation. One approach suggested is to tape the weights to the ruler and measure the time it takes for the ruler to reach its equilibrium position. However, it is also suggested to measure the frequency or period of the oscillations within the overall exponential decay damping curve. This may be done using a digital camera and stopwatch.
  • #1
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Homework Statement


I'm currently having a bit of trouble figuring out how to most effectively execute my experiment. It's somewhat practical; I need to find how the masses placed on the end of a vibrating ruler will affect its oscillation.

I know that the ruler is a standard 12 inch (30.5 cm) ruler, with 20 centimeters hanging off the edge of a desk, and that I have several weights for my use (weights range from 5g-50g)


Homework Equations



I have no idea.

The Attempt at a Solution



My idea was to simply tape the weights to the end of the ruler using lightweight scotch tape, and bending the ruler down approximately 1-2 inches from its equilibrium position, and timing how long it takes for the ruler to reach its equilibrium position at 4 or 5 different weights. Is this the most accurate way to determine how weights affects time of oscillation?
 
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  • #2
I suspect the motion will go like this Wikipedia graph for damped harmonic motion:
200px-Step_response_for_two-pole_feedback_amplifier.PNG

The measurement you suggest would be the time for the oscillations to die out.

I think it would be more interesting to measure the frequency or period of the oscillations within the overall exponential decay damping curve (dashed line). Unfortunately I can't think of an easy way to measure those. Have you got a digital camera with a video mode - if so, you may be able to video it along with a stopwatch and then watch in slow motion to see the period or count the number of oscillations in a measured time.
 

1. How does the weight placed on a ruler affect its oscillation?

The weight placed on a ruler affects its oscillation by changing the center of mass of the ruler. This shift in the center of mass causes the ruler to have a different moment of inertia, which affects its oscillation frequency.

2. What is the relationship between weight and oscillation frequency of a ruler?

The relationship between weight and oscillation frequency of a ruler is inverse. As the weight placed on the ruler increases, the oscillation frequency decreases. This is because a heavier ruler has a larger moment of inertia, making it harder to oscillate at a higher frequency.

3. How does the position of the weight on the ruler affect its oscillation?

The position of the weight on the ruler affects its oscillation by changing the distribution of mass along the ruler. Placing the weight closer to the center of mass of the ruler will result in a smaller moment of inertia and a higher oscillation frequency. On the other hand, placing the weight farther away from the center of mass will increase the moment of inertia and decrease the oscillation frequency.

4. What other factors can affect the oscillation of a ruler?

Other factors that can affect the oscillation of a ruler include the length of the ruler, the material it is made of, and the angle at which it is released. A longer ruler will have a lower oscillation frequency, while a shorter ruler will have a higher oscillation frequency. The material of the ruler can also affect its flexibility and therefore its oscillation. The angle at which the ruler is released can also impact the amplitude and frequency of its oscillation.

5. How can the results of this experiment be applied in real-life situations?

The findings from this experiment can be applied in various real-life situations such as understanding the behavior of pendulums or improving the design of structures to withstand vibrations. It can also be used in the field of engineering to optimize the design of machines that rely on oscillation, such as clocks or musical instruments.

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