Finding Position of Simple Harmonic Oscillator

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To find the position of a simple harmonic oscillator at time t=0 given initial conditions at t=1.00, one can utilize the known position, velocity, spring constant, and mass without calculating the phase constant. The problem does not specify the initial motion conditions, making it unclear whether the block started at maximum amplitude or from equilibrium. The challenge lies in deriving the position from first principles, potentially through a second-order differential equation. Solving for the phase constant is typically a straightforward method, but the constraints of the problem suggest a more fundamental approach is required. This emphasizes the importance of understanding the underlying mechanics of simple harmonic motion.
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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