The force required to stretch a spring varies directly with the amount the spring is stretched. A spring stretches by 33 m when a 19 N weight is hung from it and the weight is at rest (at equilibrium). The 19 N weight is replaced by an unknown weight W so that the spring is stetched to a new equilibrium position, 17 m below the position if no weight were attached. The weight W is then displaced from equilibrium and released so that it oscillates.

The period is  

Explanation:

From the question we are told that

   The extension of the spring is  

   The  first weight  applied is  

     The second weight applied is  

     The second extension is

The spring constant of the spring is mathematically evaluated as

substituting values

We are told that

         19 N extended the spring to 33 m    

Then W N  will extended it by  17 m

Therefore    

Generally the period of the oscillation is mathematically represented as

where M is the mass of the W which is mathematically evaluated as

substituting values