- 10

- 2

- Thread starter Ahmed Abdalla
- Start date

- 10

- 2

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

Science Advisor

- 648

- 147

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.

- 10

- 2

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.

- Replies
- 6

- Views
- 1K

- Replies
- 8

- Views
- 10K

- Replies
- 3

- Views
- 4K

- Replies
- 5

- Views
- 2K

- Replies
- 2

- Views
- 1K

- Replies
- 2

- Views
- 4K

- Replies
- 3

- Views
- 2K

- Replies
- 5

- Views
- 714

We Value Quality

• Topics based on mainstream science

• Proper English grammar and spelling

We Value Civility

• Positive and compassionate attitudes

• Patience while debating

We Value Productivity

• Disciplined to remain on-topic

• Recognition of own weaknesses

• Solo and co-op problem solving

• Topics based on mainstream science

• Proper English grammar and spelling

We Value Civility

• Positive and compassionate attitudes

• Patience while debating

We Value Productivity

• Disciplined to remain on-topic

• Recognition of own weaknesses

• Solo and co-op problem solving