Question

A block of mass m is gently attached to the spring released at time t=0

Answer 1

your question is incomplete,
              Q -- >a block of mass m is gently attached to the spring and released at time t=0 when the spring has its free length. During subsequent motion of the block,find the variation of x with respect to time.
       
solution:-  we know that spring oscillates harmonically,
    so, x' = g - ω²x 
where, ω² = k/m

at equilibrium position, xeq = g/ω² 
so, we write equations of harmonic oscillates, xeq - x = acosωt
here, a =g/ω² 
so, the equation of motion becomes, x = xeq - xeq.cosωt
                            = g/ω² - g/ω²cosωt
                            =g/ω²(1-cosωt) = mg/k (1-cosωt)
because,ω² = k/m 

hence, x = mg/k(1-cosωt) is the answer