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- Thread starter Ahmed Abdalla
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- #1

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Have a look at **[PDF]Hooke's Law - UCSB Physics**

- #3

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U(x) = U(0) + x (dU/dx)

where the subscript 0 on the derivatives means that they are evaluated at x = 0. If x = 0 is a minimum, then the first derivative in the above expansion is zero, and that leaves the quadratic term as the dominant term in the Taylor expansion of the potential energy, and is identified as the "spring" potential energy.

- #4

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Thank you that explained it in great detail!

U(x) = U(0) + x (dU/dx)_{0}+ (x^{2}/ 2!) (d^{2}U/dx^{2})_{0}+ ...(higher order terms)

where the subscript 0 on the derivatives means that they are evaluated at x = 0. If x = 0 is a minimum, then the first derivative in the above expansion is zero, and that leaves the quadratic term as the dominant term in the Taylor expansion of the potential energy, and is identified as the "spring" potential energy.

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