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.
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.
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