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If one vibration has 4.8 times the energy of a second, but their frequencies and masses are the same, what is the ratio of their amplitudes?
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E1 = 1st energy

E2 = 2nd energy = 4.8*E1

In general, the energy is related to amplitude by:

E = 1/2*k*A^2*sin^2(wt)

So...

E1 = 1/2*k*A1^2*sin^2(wt)

E2 = 1/2*k*A2^2*sin^2(wt)

Now:

E2 / E1 = 4.8 = (A2/A1)^2

or

A2/A1 = sqrt(4.8) = 2.19

The ration of the amplitudes is 2.19
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