m = mass of the weight suspended = 1 kg
x₀= stretch in the spring at equilibrium = ?
k = spring constant of the spring = 50.0 N/m
using equilibrium of force ,
spring force on the weight = force of gravity on the weight
k x₀ = mg
50 x₀ = (1 x 9.8)
x₀ = 0.196 m
x = distance by which the weight is pulled below equilibrium = 0.50 m
a = acceleration of the weight
F = spring force on the weight in upward direction ,
force equation for the motion of weight is given as
F - mg = ma
k (x + x₀) - mg = ma
(50)(0.50 + 0.196) - (1) (9.8) = 1 a
a = 25 m/s²