A block of mass m is hanging from the ceiling by a spring whose spring constant is k. Now the spring is pulled further down by x units.
Find the spring force acting on the block at that instant?
When you hang the block on the spring, it will be pulled down by block's weight downward and will have extension ′x′0.
Drawing free body diagram
Now the spring is pulled down further by x
Total extension in the spring = x0+x=(mgk+x)
So spring force = K(mgk+x)