Find the frequency of the cylinder's vertical vibration

In summary, the tension in the string affects the force of the spring, which affects the frequency of the system.
  • #1
CGI
74
1

Homework Statement


upload_2016-2-20_14-47-16.png

upload_2016-2-20_14-47-30.png


Homework Equations



w = √k/m
w = 2π/P
ƒ = 1/P

The Attempt at a Solution


I feel like I'm so close to the answer, I think it has something to do with the fact that there's a spring and pulley in the system that is throwing my answer off. I have

√k/m = 2π/P

So,

P = 2π(√m/k) Then we take the number one and divide it by P to find frequency

1/2π(√m/k) which I get to be

ƒ = √(k/m) / 2π, which is close, but not quite. The answer is actually

ƒ = √(k/m)/(4π)

Can anyone help me understand where I'm going wrong? Thank you! :)
 

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  • #2
Can you repost the figure so that the entire figure is visible?
 
  • #3
I'm not sure what you mean. The cylinder, pulley and spring is the entire figure. Or is the picture not visible?
 
  • #4
The picture is visible, but I can't tell what is at the bottom end of the string on the right side.
Edit: OK, I thought there was more to it. The string is fixed at the lower right. Sorry, I get it now.
 
  • #5
Oh, I believe the bottom of the string is attached to a fixed end.
 
  • #6
CGI said:
Oh, I believe the bottom of the string is attached to a fixed end.
Thanks.
 
  • #7
If the spring stretches by an amount Δx, what is the vertical displacement Δy of the cylinder?
 
  • #8
Would Δy = 1/2Δx?
 
  • #9
Yes. No, but you have the right idea.
 
  • #10
Okay,but how exactly would the change in displacement affect the frequency? Would the displacement affect the value of K? Therefore, changing our ω?
 
  • #11
No, the spring constant is an inherent property of the spring. k is not affected by displacements of the spring or cylinder. I spoke too soon in post 9 where I first agreed with your answer in post 8. Do you see the correct relation between Δy of the cylinder and Δx of the spring?

Next, you might consider the situation where the cylinder is hanging at rest. What is the tension in the string? What is the force of the spring? How much is the spring stretched when the cylinder is hanging at rest?
 

1. What is the frequency of a cylinder's vertical vibration?

The frequency of a cylinder's vertical vibration is the number of complete oscillations or cycles it makes in a unit of time, typically measured in Hertz (Hz).

2. How can the frequency of a cylinder's vertical vibration be calculated?

The frequency of a cylinder's vertical vibration can be calculated by dividing the number of oscillations by the time it takes to complete those oscillations. This can be done by using a stopwatch or by using specialized equipment such as a frequency meter.

3. What factors affect the frequency of a cylinder's vertical vibration?

The frequency of a cylinder's vertical vibration can be affected by several factors, including the mass and stiffness of the cylinder, the material it is made of, and the external forces acting on it.

4. How does the frequency of a cylinder's vertical vibration impact its performance?

The frequency of a cylinder's vertical vibration can affect its performance in several ways. For example, if the frequency is too high, it can cause excessive wear and tear on the cylinder, while a frequency that is too low may result in inadequate performance.

5. What are some methods used to measure the frequency of a cylinder's vertical vibration?

There are several methods used to measure the frequency of a cylinder's vertical vibration, including visual observation, timing with a stopwatch, using a frequency meter, or using specialized equipment such as a laser vibrometer.

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