1. A light spiral spring is loaded with a mass of 0.05kg and it extends by 0.10m. Determine: the period of small vertical oscillation if the value of g is 10m/s-2

This is a simple question.
Try yourself first..

You can determine the spring constant k from the data you're given. Then set up the equation of motion for a spring & mass system, using F = ma, where F = -kx, and a = d^2x/dt^2. Plug x = A*sin(wt) into the differential equation, and solve for w. That will give you the frequency of oscillation w in radians/sec , so convert that to the period of oscillation in terms of seconds.