Mass-spring system (not exactly homework)

AI Thread Summary
The discussion focuses on a mass-spring system where a mass is stretched beyond its equilibrium position. The force equation is derived as F = mg - k(x0 + x1), simplifying to F = -kx1 when equilibrium is considered. The acceleration is expressed as a = -kx1/m, leading to the relationship a = -kx1. The goal is to derive the natural frequency ω0 = √(k/m) from the acceleration equation, which involves solving the corresponding differential equation. The conversation emphasizes the mathematical transition from acceleration to the solution of the differential equation governing the system's motion.
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Case of a spring with a mass,m, that has been stretch beyond the equilibrium in the positive x direction.

mg + (-kx0) = 0
k = mg/x0

stretch:

F = mg+ [-k(x0+x1)] = mg-kx0-kx1
but since mg-kx0 = 0
F = 0-kx1 = ma

ma = -kx1
a = -kx1/m

How do I arrive at the corollary from a = - kx1/m to ω0 = SQRT[k/x]?
 
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##a = -kx_1## can be expressed as ##d^2x / dt^2 = -kx_1##

Now it comes down to fitting a solution to this differential equation...
 

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