Question

Amass undergoes SHM with an amplitude of 5.7 cm. The energy is 16 J at this time. The mass is cut in

half, and the system is again set in motion with amplitude 5.7 cm. What is the energy of the system now?

Answer 1

16 J

Step-by-step 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:

`F=-kx`

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

`E=(1)/(2)kA^2`

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.