Question 9 of 10 The data table shows how the amplitude of a mechanical wave varies with the energy it carries. Analyze the data to identify the mathematical relationship between amplitude and energy. Use your equation to find the energy if the amplitude is 8 units. Amplitude Energy 1 unit 2 units 2 units 8 units 3 units 18 units 4 units 32 units​

A         Em

     1          ½ K

     2         ½ k 4 = 2k

     3         ½ k 9 = 4.5 k

     4         ½ k 16 = 8k

Explanation:

The total mechanical energy of a simple harmonic movement is constant in time, let's look for the energy at one end of the movement, where the velocity of the body is zero.

        Em = U = ½ k x²

at the end x = A

        Em = ½ k A²

Let's build a table for the energy and as a function of the amplitudes of the movement

     A         Em

     1          ½ K

     2         ½ k 4 = 2k

     3         ½ k 9 = 4.5 k

     4         ½ k 16 = 8k

as a function of the lowest energy

      1            Eo = ½ k

      2           4Eo

      3           9 Eo

      4          16Eo

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