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