What is the amplitude of vibration for a fish on a spring scale?

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Homework Help Overview

The problem involves a fish hanging from a spring scale, which stretches under the weight of the fish. Participants are discussing the amplitude of vibration when the fish is pulled down further and released, as well as the spring stiffness constant and frequency of vibration.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to clarify the definition of amplitude and its relation to the equilibrium position of the fish. There are questions about the total displacement when the fish is pulled down and how it relates to the amplitude of vibration.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the amplitude concept. Some have provided insights into the equilibrium position and the effects of pulling the fish down, but there is no explicit consensus on the correct interpretation of amplitude in this context.

Contextual Notes

There is a focus on understanding the relationship between the spring's stretch due to the fish's weight and the additional displacement caused by pulling the fish down. The original poster's initial assumption about amplitude is being questioned.

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Homework Statement


A fisherman's scale stretches 4.1 cm when a 2.7 kg fish hangs from it.

(a) What is the spring stiffness constant?
645.3658537 N/m
(b) What will be the amplitude and frequency of vibration if the fish is pulled down 2.0 cm more and released so that it vibrates up and down?
amplitude ? cm
frequency 2.460601261 Hz


Homework Equations


I thought it was as simple as 2.0+4.1=6.1 cm. I was wrong.


The Attempt at a Solution


Shown above.
 
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The amplitude is the maximum displacement from the equilibrium position. How far from the equilibrium position is the fish when it is pulled down 2.0 cm?
 
It is already 4.1 cm away, right? Wouldn't adding 2 cm just make it 6.1 cm away?
 
You can use the period of oscillation:
[tex]T=2\pi\sqrt{\frac{m}{k}}[/tex]
then put what you found for the period in this equation:
[tex]f=\frac{1}{T}[/tex]
 
Uhh.. for amplitude?
 
With the fish on the spring the spring stretches by 4.1 cm and the fish is at rest. When the fish is at rest, it is at the equilibrium position. When the fish is pulled down by 2.0 cm it is 2.0 cm below the equilibrium position. If the fish is let go, what is the amplitude?
 

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