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The potential energy in a guitar string can be calculated from

PE = integral F dx, where x is the distance the string is stretched.

Using Hooke's Law, F=kx, where k is the elastic modulus, and x is the distance the string is stretched.

Putting it together,

PE = integral kx dx

PE = 1/2 k x^2.

The value of x varies depending on the tuning and the size of the guitar, and the value of k varies depending on the type of string used.

As an example, say a typical guitar string has a tension of about 60 Newtons, and is stretched by 5 cm. From this we can find k = 1200 kg/s^2. Fully stretched, PE = 1/2 (1200) (0.05)^2 = 1.5 Joules.

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