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In my question,I have two masses ( M ) ,one fixed at +y and the other at -y axis and both have a distance of L from the origine. The third mass (m) is located on the +x axis at the distance of X.

I know that the gravitational forces are acting on the (m) by both masses (M), The net force is on the x axis toward (-x) and magnitude of 2Fgrav and this force will accelerate the (m) toward equilibrium (Origine) and once it is there the Fgrav =0 but because it has a velocity it will continue until its velocity=0 , So this Fgrav force on the X axis is Restoring force .Therefore,the mass will oscilate. My question is since my equation is

(x:+2GMmx/(L^2+X^2)^3/2=0) , I cant say this is Simple harmonic oscilation because my equation of motion doesnt just consist of x but x/(...+x^2)^3/2,

So under what condition for x ,it is possible to say that the motion of the mass (m) can be approximated as Simple harmonic motion ?

Any idea?

thanks

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# Homework Help: Would mass oscilate ?

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