Finding Position of Simple Harmonic Oscillator

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SUMMARY

The discussion revolves around determining the position of a Simple Harmonic Oscillator (SHO) at time t=0, given initial conditions at t=1.00, including position, velocity, spring constant, and mass. The participant has successfully calculated the maximum amplitude but is challenged by the requirement to avoid solving for the phase constant. The consensus is that while the phase constant is typically essential for solving SHO problems, the task can be approached using first principles, specifically through the formulation of a second-order differential equation.

PREREQUISITES
  • Understanding of Simple Harmonic Motion (SHM) principles
  • Familiarity with second-order differential equations
  • Knowledge of spring constant and mass relationship in oscillatory systems
  • Basic concepts of amplitude and velocity in SHM
NEXT STEPS
  • Study the derivation of the second-order differential equation for Simple Harmonic Motion
  • Explore techniques for solving SHO problems without phase constants
  • Learn about energy conservation principles in oscillatory systems
  • Investigate the relationship between amplitude, velocity, and position in SHM
USEFUL FOR

Students and educators in physics, mechanical engineers, and anyone interested in the mathematical modeling of oscillatory systems.

Andrusko
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I have been given at t=1.00 a position and velocity. And the spring constant and mass.

I have found the maximum amplitude.

The question is, where was the block at time t=0? And apparently this can be done without solving for the phase constant and making an equation.

The question doesn't specify how the block was put into motion. So I don't think you can assume that it started at it's maximum amplitude or was subjected to a force from it's equilibrium. And that's as far as I have got in solving this problem.

Is it possible without finding phase constant? Any hints/help?
 
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Why wouldn't you just solve for the phase constant?
 
The question specifies that I shouldn't do that. I think it's some kind of challenge to do it from first principles. Like making a second order differential equation.
 

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