Energy of the Simple Harmonic Oscillator

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Homework Help Overview

The discussion revolves around the energy of a simple harmonic oscillator, specifically analyzing the motion of a mass attached to a spring. The original poster presents a problem involving a mass, spring constant, and displacement, seeking to find the speed of the mass at a specific displacement.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of conservation of energy principles, questioning how to express energy at a given displacement. There is an exploration of kinetic and potential energy relationships, with some participants attempting to derive equations related to energy at specific points in the oscillation.

Discussion Status

The discussion is ongoing, with participants providing hints and guidance regarding the relationship between total mechanical energy, kinetic energy, and potential energy. There are multiple interpretations of how to approach the problem, particularly concerning the potential energy at various displacements.

Contextual Notes

Participants are navigating the constraints of the problem, including the need to express energy in terms of displacement and the implications of using specific energy equations. There is a noted uncertainty regarding the correct application of kinetic and potential energy formulas.

adashiu
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A 50.0-g mass connected to a spring with a force constant
of 35.0 N/m oscillates on a horizontal, frictionless
surface with an amplitude of 4.00 cm. Find the speed of the mass
when the displacement is 1.00 cm.

Can I use here something like :

\frac{mv2}{2}=0,5kx2?
 
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Use conservation of energy. What's the total energy at any point in the motion?
 
The total energy is 0,5kA2=0,028

But how to express an energy at displacement 1cm? :blushing:
 
Hint: Total mechanical energy is the sum of kinetic and potential energy.
 
Yes i know that but there is no formula with velocity...

I've got to use mv2/2??
 
adashiu said:
Yes i know that but there is no formula with velocity...

I've got to use mv2/2??
Yes, that's the kinetic energy. What's the potential energy at any point?
 
Potential energy is 0?
 
adashiu said:
Potential energy is 0?

Total energy is : 0,5kA2=4*10-5

mv22/2=4*10-5

v=0.04, of course it seems not to be correct :(
No. Hint: Potential energy is zero when x = 0 and maximum at x = A. What's the PE at an arbitrary position?
 
adashiu said:
\frac{mv2}{2}=0,5kx2


?
Your equation defines a condition when a half of the energy is in speed and another half in the displacement.
Ek + Ep = E
E = kA2/2
mv2/2 = E - kx2/2
 

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