A particle of mass $m$ is oscillating with simple harmonic motion - AQA - A-Level Physics - Question 31 - 2021 - Paper 1

The maximum kinetic energy ( $K_{max}$) of a particle undergoing simple harmonic motion can be derived from the formula:

K_{max} = rac{1}{2} k A^2

Where:

• $k$ is the spring constant, and can also be expressed as k = rac{4\pi^2 m}{T^2}

By substituting the value of $k$, we have:

K_{max} = rac{1}{2} rac{4eta^2 m}{T^2} A^2 = rac{2 m A^2}{T^2}

Thus, the maximum kinetic energy of the particle is:

K_{max} = rac{2 m A^2}{T^2}

This means that the correct option from the provided choices is D: $\frac{2 \pi^2 m A^2}{T^2}$.