An object of mass 2.0 kg is attached to the top of a vertical spring that is anchored to the floor. The unstressed length of the spring is 8.0 cm and the length of the spring when the object is in equilibrium is 5.9 cm. When the object is resting at its equilibrium position, it is given a sharp downward blow with a hammer so that its initial speed is 0.30 m/s. (a) To what maximum height above the floor does the object eventually rise

The value is

Explanation:

From the question we are told that

    The mass of the object is  

    The unstressed length of the string is  

    The length of the spring when it is  at equilibrium is  

      The initial speed (maximum speed)of the spring when given a downward blow

Generally the maximum speed  of the spring  is mathematically represented as

Here A is maximum height above the floor (i.e the maximum amplitude)

            and is the angular frequency which is mathematically represented as

So

=>      

Gnerally the length of the compression(Here an assumption that the spring was compressed to the ground by the hammer is made) by the hammer is mathematically represented as

=>        

=>        

Generally at equilibrium position the net force acting on the spring is  

=>        

=>        

So

=>