Question

In an oscillation, why does removing mass at the equilibrium point decrease the amplitude? I understand that it is because the total energy is equal to kinetic energy at the equilibrium and decreasing mass decreases kinetic energy and thus decreases the amplitude but I do not know how to mathematically prove this.

Answer 1

Solution:

The kinetic energy at the equilibrium position is obtained at the expense of the potential energy spring mass system had at the extreme position.

Kinetic energy, K = U, potential energy at the extreme position.

Consider a simple spring mass system

If M is decreased, so will A = amplitude.