Answer:
16 J
Explanation:
A system in Simple Harmonic Motion (SHM) is a system oscillating periodically around an equilibrium position, and having a restoring force proportional to the displacement that brings the system back towards the equilibrium position:
[tex]F=-kx[/tex]
where
k is the spring constant of the system
x is the displacement wrt the equilibrium position
In a SHM, the total energy of the system is given by the equation
[tex]E=\frac{1}{2}kA^2[/tex]
where
k is the spring constant of the system
A is the amplitude of motion (the maximum displacement)
In this problem, the initial energy of the system is
E = 16 J
when the amplitude is A = 5.7 cm.
Later, the mass is cut in a half, while the amplitude remains the same: A = A' = 5.7 cm.
However, we see that the energy in a SHM does not depend on the mass: therefore, since the amplitude has remained constant, the energy will remain the same.
