- #1
Natural Frequency: Find Equation of Motion
- Thread starter mrblanco
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Discussion Overview
The discussion revolves around finding the natural frequency of a block-lever-spring system, with a focus on deriving the equation of motion. Participants explore the dynamics of the system, including the effects of multiple springs and a lever mechanism.
Discussion Character
- Homework-related
- Exploratory
- Technical explanation
- Debate/contested
Main Points Raised
- Some participants inquire about the initial equations and the nature of harmonic motion in the system, particularly how the lever affects the block's movement.
- There is a suggestion to consider the resonant frequency of the block with only one spring connected, raising questions about how to approach the problem.
- Participants discuss the equation rF1+/-rF2=I(alpha) and its relevance to finding the natural frequency, with some expressing uncertainty about its derivation.
- One participant notes that moving the block to the right compresses both springs, leading to a discussion about whether the springs work against or with each other due to the lever's mechanics.
- There is a mention of the mechanical advantage provided by the vertical lever and the significance of the ratio of certain parameters in the system.
- Participants explore the implications of having springs in series versus parallel, questioning how these configurations affect the overall spring constant and system behavior.
Areas of Agreement / Disagreement
Participants express differing views on the interaction between the springs and the lever, with some suggesting they work against each other while others propose they may be effectively combined into a single spring constant. The discussion remains unresolved regarding the exact nature of these interactions and their impact on the equation of motion.
Contextual Notes
Participants acknowledge missing values and assumptions in their analysis, which may affect their conclusions. The discussion includes unresolved mathematical steps and varying interpretations of the system's dynamics.
- #2
berkeman
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mrblanco said:
Welcome to the PF.
So what are your initial equations? What does the harmonic motion of the block look like, and how is it affected by the part with the levers?
- #3
mrblanco
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This is all the information I was given. The block is moving to the left but no values are given. The middle lever has a pin connection
- #4
berkeman
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mrblanco said:
Well if you only had the spring on the right connected to the block, how would you calculate the resonant frequency?
- #5
mrblanco
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Also, I know I have to use rF1+/-rF2=I(alpha) just not sure how
- #6
berkeman
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mrblanco said:
Where does that come from? Why do you think it is a way to get to the natural frequency of this block/lever/spring system?
- #7
mrblanco
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I'm thinking that has to be part of the equation of motion for the block
- #8
mrblanco
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If I only considered the spring on the right, I get a complex answer...
- #9
berkeman
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mrblanco said:
I'll ask again -- what is the resonant frequency of just a single block and spring? -- EDIT -- I see you added that.
And then, what is the action of the lever and the lower spring? Does that force oppose or add to the motion of the block? What do the two sides of the vertical bar (on either side of the fulcrum) do to the level of the 2nd spring's force as applied to the block?
- #10
berkeman
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mrblanco said:
That's correct for a single spring and mass (except for the negative sign inside the square root).
http://hyperphysics.phy-astr.gsu.edu/hbase/shm2.html
.
- #11
mrblanco
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- #12
berkeman
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mrblanco said:
I believe the function of the vertical lever is like a lever arm -- it gives mechanical advantage. What significance does the ratio of a and b have?
- #13
mrblanco
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- #14
berkeman
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mrblanco said:
I think you're on the right track, but look closer at how the force of the left spring is translated through the vertical lever & fulcrum...
If you grab ahold of the block and push it to the right, that compresses the right spring, correct? What does it do to the left spring at the same time? Are the springs working against each other or with each other? How does that change your differential equation?
- #15
mrblanco
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If i move the block to the right that would also compress the k2 spring. Aren't the springs working against each other because of the lever? When one pulls in one direction, the other pulls in the opposite direction.
I know I'm missing something here but I can't seem to figure it out
I know I'm missing something here but I can't seem to figure it out
- #16
berkeman
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mrblanco said:
You're doing fine. Moving the block to the right compresses both springs. So you might as well have one spring on the right only, with what overall spring constant?
- #17
mrblanco
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Springs in series so 1/k +1/k2
- #18
berkeman
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mrblanco said:
Does putting springs in series make them stronger or weaker? Does putting springs in parallel make them stronger or weaker?
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