Answer:
The greatest extension of the spring is  and the maximum speed of the block is
 and the maximum speed of the block is  .
.
Explanation:
Given:
The mass of the block is, 
The spring constant of the spring is, 
The mechanical energy of the block is, 
When a particle is oscillating in a simple harmonic way, its total energy is given by

where  is the angular velocity of the mass and
 is the angular velocity of the mass and  is the amplitude of its motion.
 is the amplitude of its motion.
The relation between angular velocity and spring constant is given by

Substituting equation (2) in equation (1), we have

Substituting  for
 for  and
 and  for
 for  in equation (3), we can write
 in equation (3), we can write

The relation between the maximum velocity and the amplitude is given by

Substituting  for
 for  ,
 ,  for
 for  and
 and  for
 for  in equation (4), we have
 in equation (4), we have
