Max Speed of Mass on Spring: Calculate Vmax with 2πfA

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Homework Help Overview

The problem involves determining the maximum speed (Vmax) of a mass attached to a spring, specifically exploring the relationship expressed by the formula 2πfA. The context is rooted in concepts of oscillatory motion and energy conservation.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss using conservation of energy to relate potential and kinetic energy without calculus. There are inquiries about the appropriate equations for simple harmonic motion and the general equation of motion.

Discussion Status

The discussion is ongoing, with some participants providing guidance on using energy conservation principles. Others are seeking clarification on the correct equations to apply, indicating a mix of understanding and confusion regarding the topic.

Contextual Notes

One participant notes their lack of calculus knowledge, which may limit their ability to engage fully with the problem. There is also mention of the relationship between frequency, spring constant, and mass, suggesting that these concepts are under consideration.

Mary1910
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Prove that the maximum speed (Vmax) of a mass on a spring is given by 2πfA.

I have no idea how to solve this problem. I have not taken calculus yet, and I am really confused on how to come up with a solution for this. Any help would be appreciated. Thanks
 
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With conservation of energy, you can solve it without Calculus. Compute max potential energy. Set equal to max kinetic energy. Solve for v.
 
As Dr. Courtney says, but first you need to quote the general equation for the motion.
 
Ok I'm still lost. Should I be using, E=½mv^2 + ½kx^2 for the general equation for the motion?
 
Mary1910 said:
Ok I'm still lost. Should I be using, E=½mv^2 + ½kx^2 for the general equation for the motion?
No, that's just conservation of energy in a spring. What's the equation of simple harmonic motion? Or, you can use the above equation if you know the relationship between f, k and m for a spring.
 
haruspex said:
What's the equation of simple harmonic motion?

Hooke's Law: F=-kx
 
The general equation of motion should have a sine or cosine in it.
 

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