Hi there!
Recall that the amplitude of an oscillating system occurs at a point of maximum potential energy.
For a spring system, potential energy is given as:
[tex]U = \frac{1}{2}kx^2[/tex]
U = Potential Energy (J)
k = Spring constant (N/m)
x = amplitude (m)
We can rearrange the equation to solve for amplitude more easily.
[tex]U = \frac{1}{2}kx^2\\\\2U = kx^2\\\\x^2 = \frac{2U}{k}\\\\x = \sqrt{\frac{2U}{k}}[/tex]
If we double 'U':
[tex]x' = \sqrt{\frac{2(2U)}{k}} = \sqrt{2}*\sqrt{\frac{2U}{k}}\\\\x' = \sqrt{2} * x[/tex]
Thus, the new amplitude would be √2 times greater, so:
[tex]20 cm \cdot \sqrt{2} = \boxed{28.284 cm}[/tex]
