Angular frequency is 2 not 4π .
why u subtracted a net? @Mayank_Chowdhary
The Fnet acting on the object will be the external force - the force causing SHM
But why ?
But the direction of force isn't mentioned why you took it on the right? @Mayank_Chowdhary
It will change according to time sin(t)
So it will be acting in forward direction for the belongs to [0, π]
However kx will always be towards origin
So basically it will be always in opposite direction of kx
This is actual Jee main question you dont need to solve complete ,this question is meant to be solved by options
Eliminate options by putting t=0, X should be zero and velocity non zero ( For SHM)
Oops thanks bro @Mayank_Chowdhary