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Homework Statement
There is a particle that moves in 1dimension. mass is m, force on the object is given as a function of position(x), F_{x}= mω^{2}x.(ω is constant) when t=0 particle has x_{0}>0, and velocity is zero. find the particle's position as a function of time.
Homework Equations
There is a given hint for the problem. Use z=Acosu conversion on this integral
The Attempt at a Solution
What i did so far: I used Newton's second law so that i can find accerelation. Then i integrate accerelation function and find velocity function as a function of position. Lastly i integrate velocity function and i find x= x_{0} ω^{2}x^{3}/6. From there i can't do anything. I couldn't use motion equations because accerelation is not constant. And i couldn't find how to use this integral.
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