- #1

Winvoker555

## Homework Statement

Two springs which have spring constant of

**k1**and

**k2**respectively are vertically hung in a series. Then, a mass

**m**is attached to the end. Find the displacement and the spring constant of this series.

## Homework Equations

## The Attempt at a Solution

I got the displacement

**x**right (which is equal to

_{1}+x_{2}**mg/k**).

_{1}+mg/k_{2}Then, I solved for the series constant by using the conservation of energy ,and let the two springs be my system.

**ΔU**

_{s}= W_{ext}**ΔU**

k(x

k(x

k = 2mg/(x

_{s}= mg⋅(x_{1}+x_{2})k(x

_{1}+x_{2})^{2}/ 2 = mg(x_{1}+ x_{2})k(x

_{1}+x_{2}) / 2 = mgk = 2mg/(x

_{1}+ x_{2})Since

**x**,then

_{1}+x_{2}= mg / k_{1}+mg / k_{2})**:**

**k = 2mg / (mg / k**

_{1}+ mg / k_{2})**k = (2k**

_{1}k_{2}) / (k_{1}+k_{2})I checked the solution and this is not correct (the correct answer is

**(k**);also, I know that the formula for spring constant of a series of two springs is 1 / k

_{1}k_{2}) / (k_{1}+k_{2})_{series}= 1 / k

_{1}+ 1 / k

_{2}. However, I can't figure out what I did wrong and what caused the extra 2 factor in the numerator.