Doubt in mechanics

help here guys. @Seshank
ans is AC

i have a very kasht wala method bro…
first take acceleration of centre of mass then take relative acceleration of m1 w.r.t cm
fir uske bad find the “new” spring constant wrt com fir uske bad ans ayega
if anyone has a short method or I post mine…

@PotatoSauce you can post yours

The first option can easily be calculated via CoM and reduced mass of the system

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Small correction @Abhinav.08
The elongation produced by the two forces will not be the same ( x/2).Rather take it x1 and x2.Answer won’t change.

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jst did’t get why the elongation will not be same…if we are considering a single spring on which equal and opp forces are acting

while conserving energy you have used
Fx1 + Fx2 = 1/2 Keq (x1+x2)^2


@Abhinav.08 masses aren’t equal,that is why.