A particle of mass m undergoes simple harmonic motion with amplitude A and frequency f - AQA - A-Level Physics - Question 24 - 2020 - Paper 1

The total energy E of a particle undergoing simple harmonic motion is given by the formula:

E = rac{1}{2} k A^2

where k is the spring constant. However, we can also express k in terms of the mass m and the angular frequency (\omega = 2\pi f):

$k = m (2 \pi f)^2$

Substituting this back into the energy formula gives:

E = rac{1}{2} m (2 \pi f)^2 A^2

This simplifies to:

$E = 2 \pi^2 m f^2 A^2$

From the options given, we compare this with the choices provided and find that the correct representation for the total energy is:

$E = 4 \pi^2 m f^2 A^2 / 2 = 2\pi^2 m f^2 A^2$

Thus, the total energy is represented by option C: $4 \pi m f^2 A^2$.