A block of known mass is suspended from a fixed support through a light spring. Can you find the time period of vertical oscillation only by measuring the extension of the spring when the block is in equilibrium?

Yes, the time period of the vertical oscillations in the spring can be determined. The time period of a simple pendulum is shown below. When pendulum is replaced by spring, them mg=kx. Hence, by determining the extension in the spring, the time period can be obtained.