Classical Mechanics: Simple harmonic oscillator problem

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Homework Help Overview

The discussion revolves around a simple harmonic oscillator problem involving a mass and spring system. The original poster presents a scenario where the mass is projected towards the origin from a specific position with an initial speed, seeking the equation of motion.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to determine the amplitude and phase of the motion using the initial conditions provided. Some participants suggest using conservation of energy to find the amplitude, while others question the relationship between angular frequency and the given parameters.

Discussion Status

Participants are exploring different methods to approach the problem, with some offering guidance on using energy conservation to find the amplitude. There is an ongoing examination of the equations involved, and one participant has proposed a potential solution, although it remains unclear if it aligns with the initial conditions.

Contextual Notes

There is a noted challenge due to the presence of multiple unknowns and the need for additional equations or relationships to fully resolve the problem. The original poster expresses uncertainty about the next steps in their reasoning.

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Homework Statement


A simple harmonic oscillator with mass m = 1/2 and k = 2 is initially at the point
x = √3 when it is projected towards the origin with speed 2.
Find the equation of motion describing x(t).


Homework Equations



x=Asin(ωt+θ)


The Attempt at a Solution



At t=0, x=√3

√3=Asin(θ)

There is two unknowns and only one equation...I'm stuck
 
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You just need to use a little ingenuity to solve for A.

You know that the mass is projected towards the eq point from x=sqrt(3) with velocity 2. Since you know the spring constant and the mass, you can find the mass's total energy, and thus it's position (A) at maximum extension using conservation of energy.
 
Do you recognise that ω = √k/m ?
 
K, well I did a lot of work on white board and my conclusion is:
x(t)=2sin(4t-pi/3)
Does this make sense? Do you need to see all my work?
 

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