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

Updated: 9/26/2023

Joshgeurts7

Lvl 1
7y ago

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

Wiki User

7y ago

Wiki User

7y ago

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.

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