Question

@Kainui @Mashy @ganeshie8 , Please help

Answer 1

use below
\[F = -kx \implies \dfrac{d^2x}{dt^2} = -\frac{k}{m}x\]

Answer 2

plugin each option and see which one satisfies the above DE

Answer 3

it is easy to see that first option satisfies if you're familiar with a well known trig identity
\[a\cos x + b\sin x = R\sin \alpha \]