The ratio of their amplitudes is 3.
The relation between energy and amplitude is as follows:
[tex]E_{1} = \frac{1}{2} KA_{1} ^{2}[/tex]
[tex]E_{2} =\frac{1}{2} KA_{2} ^{2}[/tex]
As, we know , one oscillation has 3.0 times the energy of a second one of equal frequency and mass i.e.,
[tex]E_{1} = 3E_{2}[/tex]
So, [tex]\frac{1}{2} KA_{1} ^{2} = 3(\frac{1}{2}KA_{2} ^{2} )[/tex]
[tex]A_{1} ^{2} = 3A_{2} ^{2}[/tex]
[tex]\frac{A_{1}^{2} }{A_{2}^{2} } = 3[/tex]
Therefore, the ratio of their amplitudes is 3.
Learn more about amplitude here:
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