Where does the relationship Energy is proportional to Amplitude squared come from?

Answer 1

In case of simple harmonic motion the velocity max at the equilibrium will be a w

Here w (omega) is the angular frequency = 2 pi nu (frequency)

Now kinetic energy E = 1/2 m v^2 = 1/2 * m * a^2 * w^2

Here a is amplitude.

So energy seems proportional to the square of amplitude

Answer 2

It really depends on the specific situation. In some cases, it is related to the fact that energy is proportional to the fact that kinetic energy is proportional to the square of the speed - at higher amplitudes, the particles will also move at greater speeds.

Answer 3

This relationship comes from the energy conservation principle in wave mechanics. For a wave, the energy is proportional to the square of the amplitude because energy is a scalar quantity and is directly related to the square of the wave's amplitude. This relationship holds for various types of waves, including electromagnetic waves and sound waves.