Physics

Problem

Two identical particles execute simple harmonic motion with the same angular frequency but different amplitudes

A_{1}=0.10\,\text{m}

and

A_{2}

. At a displacement of

0.05\,\text{m}

from their respective mean positions, the ratio of their kinetic energies is

1:3

(first to second). What is the value of

A_{2}

? a)

0.25\,\text{m}

0.16\,\text{m}

0.19\,\text{m}

0.17\,\text{m}

Intuitive explanation

The key insight is that kinetic energy in SHM depends on both the amplitude and the current displacement through energy conservation. At any position $x$ , the kinetic energy is $KE = \frac{1}{2}m\omega^2(A^2 - x^2)$ , which comes from the total mechanical energy minus potential energy. Since both particles have the same mass and frequency but different amplitudes, you can set up a ratio of their kinetic energies at the same displacement and solve for the unknown amplitude.

Intuitive explanation

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