Answer:
The greatest extension of the spring 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 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
and
for
in equation (3), we can write

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

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